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Journal articles on the topic 'Their ideals'

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Published: 4 June 2025

Last updated: 15 July 2025

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1

Wheelock, Lucy. "Ideas and Ideals." Childhood Education 93, no. 3 (2017): 189–92. http://dx.doi.org/10.1080/00094056.2017.1325219.

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2

SANDERS, CATHERINE. "IDEAS, IDEALS AND INNOVATIONS." Australian and New Zealand Journal of Family Therapy 11, no. 4 (1990): iii. http://dx.doi.org/10.1002/j.1467-8438.1990.tb00821.x.

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3

YANG, DONG-WHEE. "Issues in Chomsky's Ideas and Ideals (N. Smith, Chomsky: Ideas and Ideals)." ENGLISH LINGUISTICS 18, no. 2 (2001): 696–719. http://dx.doi.org/10.9793/elsj1984.18.696.

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4

Hunter, Allen, and Krishan Kumar. "1989: Revolutionary Ideas and Ideals." Contemporary Sociology 32, no. 1 (2003): 87. http://dx.doi.org/10.2307/3089868.

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5

Hoffman, Mary. "Ideas and Ideals from Experience." Music Educators Journal 76, no. 1 (1989): 26–29. http://dx.doi.org/10.2307/3400895.

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6

Guo, Jin, and Tongsuo Wu. "Monomial Ideals under Ideal Operations." Communications in Algebra 43, no. 11 (2015): 4745–62. http://dx.doi.org/10.1080/00927872.2014.952012.

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7

Edwards, Harold M. "Mathematical ideas, ideals, and ideology." Mathematical Intelligencer 14, no. 2 (1992): 6–19. http://dx.doi.org/10.1007/bf03025208.

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8

Milsark, Gary L. "Chomsky: Ideas and Ideals (review)." Language 77, no. 3 (2001): 599–600. http://dx.doi.org/10.1353/lan.2001.0177.

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9

Rudin-Jones, C., K. Hegan, C. Smith, J. Ashton-Martyn, and D. W. Beaven. "Interdisciplinary teams — ideas, ideals, innovations." Patient Education and Counseling 23 (June 1994): S91. http://dx.doi.org/10.1016/0738-3991(94)90325-5.

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10

Patil, Jitendrasing J. "On Regular and Intra-Regular Γ-Semihyperrings-II". Int. Res. Journal of Science & Engineering, 2023 11, № 5 (2023): 191–97. https://doi.org/10.5281/zenodo.10076216.

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In this paper we have proved some results on regular and intra-regular Γ-semihyperring. The characterization of regular and intra-regular Γ-semihyperring with the help of quasi-ideals, bi-ideals, prime bi-ideals and irreducible bi-ideals of Γ-Semihyperrings. 

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11

Tilak, Raj Sharma, and Sharma Ritu. "Prime Fuzzy Ideals of a Gamma Semiring -1." Indian Journal of Science and Technology 16, no. 31 (2023): 2441–46. https://doi.org/10.17485/IJST/v16i31.1333.

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Abstract <strong>Objectives:</strong> The main objective of this article is to introduce some fundamental results of fuzzy ideals and Prime fuzzy ideals of a G􀀀 semiring R . <strong>Methods:</strong> We use some fundamental results of fuzzy ideals and conditions like semi subtractive, centreless etc. for developments of the main results. <strong>Findings:</strong> In this connection, we establish some important results of fuzzy ideals and prime fuzzy ideals of semirings to G􀀀 semirings. <strong>Novelty:</strong> We find a special class of fuzzy ideals of a G􀀀 semiring R and with this, construct a lattice ordered G􀀀 semiring. Further, we find that a fuzzy ideal of G􀀀 semiring R can be a decreasing map from [0, 1] into the set of R together with an empty set. As an application of this result, the prime fuzzy ideals of a G􀀀semiring R are described in terms of prime ideals of a G􀀀 semiring R. <strong>Keywords:</strong> Fuzzy Ideals; Prime Ideals; Prime Fuzzy Ideals; Lattice Ordered G- Semiring; Strong Ideal

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12

Abdulqadr, Fryad H. "Ideal Graphs Supported By Given Ideals of Commutative Rings." Journal of Zankoy Sulaimani - Part A 22, no. 1 (2020): 217–22. http://dx.doi.org/10.17656/jzs.10786.

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13

R. Nagarajan, K. Balamurugan,. "Fermatean Uncertainty Soft Sub Algebra in terms of Ideal Structures." Tuijin Jishu/Journal of Propulsion Technology 44, no. 4 (2023): 1163–74. http://dx.doi.org/10.52783/tjjpt.v44.i4.996.

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Ideal concepts are discussed in many mathematical applications. Various author has been studied and analytical in different ways. In this article, the idea of bipolar fermatean uncertainty sub algebra’s in terms of R-ideals is planned. Also the correlation among bipolar fermatean uncertainty soft ideal and bipolar fermatean uncertainty soft R-ideals is expressed some interesting ideas also analyzed.

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14

M., Palanikumar and K. Arulmozhi. "On various almost ideals of semirings." Annals of Communications in Mathematics 4, no. 1 (2021): 17–25. https://doi.org/10.5281/zenodo.10048905.

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In this paper, we study various almost ideals (shortly A -ideals), quasi A - ideals, bi quasi A -ideals, tri A -ideals and tri quasi A -ideals in semiring and give some characterizations. Some relevant counter examples are also indicated. We develop the implications ideal =⇒ quasi ideal =⇒ bi quasi ideal =⇒ tri quasi ideal =⇒ tri quasi A -ideal =⇒ bi quasi A -ideal =⇒ bi A -ideal =⇒ quasi A -ideal =⇒ A -ideal and reverse implications do not holds with examples. We show that the union of A -ideals (bi A -ideals, quasi A -ideals, bi quasi A -ideals) is a A -ideal (bi A -ideal, quasi A -ideal, bi quasi A -ideal) in semiring.

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15

MESYAN, ZACHARY. "THE IDEALS OF AN IDEAL EXTENSION." Journal of Algebra and Its Applications 09, no. 03 (2010): 407–31. http://dx.doi.org/10.1142/s0219498810003999.

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Given two unital associative rings R ⊆ S, the ring S is said to be an ideal (or Dorroh) extension of R if S = R ⊕ I, for some ideal I ⊆ S. In this note, we investigate the ideal structure of an arbitrary ideal extension of an arbitrary ring R. In particular, we describe the Jacobson and upper nil radicals of such a ring, in terms of the Jacobson and upper nil radicals of R, and we determine when such a ring is prime and when it is semiprime. We also classify all the prime and maximal ideals of an ideal extension S of R, under certain assumptions on the ideal I. These are generalizations of earlier results in the literature.

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16

Biblarz, Timothy J., and Judith Stacey. "Ideal Families and Social Science Ideals." Journal of Marriage and Family 72, no. 1 (2010): 41–44. http://dx.doi.org/10.1111/j.1741-3737.2009.00682.x.

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17

Zubkov, Artem. "Ideas and Ideals of Open Education." Ideas and Ideals 15, no. 4-1 (2023): 203–16. http://dx.doi.org/10.17212/2075-0862-2023-15.4.1-203-216.

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This article examines the phenomenon of open education, its infl uence, and prospects within the context of contemporary education. An in-depth exploration of this pedagogical approach offers invaluable insights for educators, researchers, policymakers, and other stakeholders intrigued by advanced methodologies and ideas in the educational realm. The primary objective of the research is to ascertain how the principles of open education facilitate the transformation of traditional educational frameworks and how they can promote educational equity. To achieve this aim, the author employs a method of analyzing diverse sources and practical examples. It is posited that open education represents a signifi cant stride towards creating a more inclusive and accessible educational milieu, anchored in the principles of democracy, self-organization, and knowledge equality. The article’s key fi ndings encompass the understanding that open education, rooted in principles of accessibility, inclusivity, self-organization, and knowledge democratization, offers novel opportunities for the transformation of conventional education and the realization of educational fairness. Challenges in implementing open education, including digital disparity, content quality, accreditation, and student motivation, are also illuminated. Open education introduces pedagogical innovations, infusing elements of fl exibility and individualization. Novelty contributions of the research encompass delineating the impact of open education on transforming educational frameworks, a profound comprehension of open education principles and their application for ensuring educational equity, and the formulation of new methodological approaches to studying the open education phenomenon. In conclusion, the study offers valuable perspectives on the role and position of open education in the current educational landscape and its potential for further exploration. This work will be of interest to those seeking to understand and probe the possibilities that open education presents for today’s educational environment.

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18

M., Palanikumar and K. Arulmozhi. "New approach towards A-ideals in ternary semirings." Annals of Communications in Mathematics 4, no. 2 (2021): 114–25. https://doi.org/10.5281/zenodo.10049057.

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To interact somebody with someone various almost ideals (shortly A -ideals), quasi A -ideals, bi quasi A -ideals, tri A -ideals and tri quasi A -ideals in ternary semiring and give some characterizations. We develop the implications ideal =⇒ quasi ideal =⇒ two sided bi quasi ideal =⇒ two sided tri quasi ideal =⇒ two sided tri quasi A -ideal =⇒ two sided bi quasi A -ideal =⇒ bi A -ideal =⇒ quasi A -ideal =⇒ A -ideal and reverse implications do not holds with examples. We show that the union of A -ideals (bi A -ideals, quasi A -ideals, bi quasi A -ideals) is a A -ideal (bi A -ideal, quasi A -ideal, bi quasi A -ideal) in ternary semiring. 

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19

Muhiuddin, G., A. M. Alanazi, A. Mahboob, and D. Al-Kadi. "Generalized Hesitant Fuzzy Ideals in Semigroups." Journal of Mathematics 2020 (December 22, 2020): 1–12. http://dx.doi.org/10.1155/2020/8856287.

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In this paper, as a generalization of the concepts of hesitant fuzzy bi-ideals and hesitant fuzzy right (resp. left) ideals of semigroups, the concepts of hesitant fuzzy m , n -ideals and hesitant fuzzy m , 0 -ideals (resp. 0 , n -ideals) are introduced. Furthermore, conditions for a hesitant fuzzy m , n -ideal ( m , 0 -ideal, 0 , n -ideal) to be a hesitant fuzzy bi-ideal (right ideal, left ideal) are provided. Moreover, several correspondences between bi-ideals (right ideals, left ideals) and hesitant fuzzy m , n -ideals ( m , 0 -ideals, 0 , n -ideals) are obtained. Also, the characterizations of different classes of semigroups in terms of their hesitant fuzzy m , n -ideals and hesitant fuzzy m , 0 -ideals ( 0 , n -ideals) are investigated.

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20

V., Amarendra Babu, Abida Begum K., and Siva Naga Malleswari V. "MBJ-Neutrosophic Positive Implicative LI-ideals, Associative LI-ideals, and Fantastic LI-ideals." International Journal of Neutrosophic Science 21, no. 2 (2023): 84–97. http://dx.doi.org/10.54216/ijns.210208.

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The MBJ-Neutrosophic positive implicative LI-ideals, the MBJ-Neutrosophic associative LI-ideals, and the MBJ-Neutrosophic fantastic LI-ideals are all introduced in this study. Of all these ideals, several their qualities and corresponding conditions were explored. We have demonstrated how every positive implicative MBJ-Neutrosophic LI-ideal evolved into an MBJ-Neutrosophic LI-ideal, MBJ-Neutrosophic implicative LI-ideal, and MBJ-Neutrosophic fantastic LI-ideal. Additionally, it was demonstrated that any MBJ-Neutrosophic fantastic LI-ideal is a MBJ-Neutrosophic associative LI-ideal.

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21

Mustaţă, Mircea, and Ken-Ichi Yoshida. "Test Ideals Vs. Multiplier Ideals." Nagoya Mathematical Journal 193 (2009): 111–28. http://dx.doi.org/10.1017/s0027763000026052.

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AbstractThe generalized test ideals introduced in [HY] are related to multiplier ideals via reduction to characteristic p. In addition, they satisfy many of the subtle properties of the multiplier ideals, which in characteristic zero follow via vanishing theorems. In this note we give several examples to emphasize the different behavior of test ideals and multiplier ideals. Our main result is that every ideal in an F-finite regular local ring can be written as a generalized test ideal. We also prove the semicontinuity of F-pure thresholds (though the analogue of the Generic Restriction Theorem for multiplier ideals does not hold).

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22

Safaeeyan, S., and A. Taherifar. "d-ideals, f d-ideals and prime ideals." Quaestiones Mathematicae 42, no. 6 (2018): 717–32. http://dx.doi.org/10.2989/16073606.2018.1486338.

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23

SOYLU YILMAZ, Elis. "4-Dimensional 2-Crossed Modules." Journal of New Theory, no. 40 (September 30, 2022): 46–53. http://dx.doi.org/10.53570/jnt.1148482.

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In this work, we defined a new category called 4-Dimensional 2-crossed modules. We identified the subobjects and ideals in this category. The notion of the subobject is a generalization of ideas like subsets from set theory, subspaces from topology, and subgroups from group theory. We then exemplified subobjects and ideals in the category of 4-Dimensional 2-crossed modules. A quotient object is the dual concept of a subobject. Concepts like quotient sets, spaces, groups, graphs, etc. are generalized with the notion of a quotient object. Using the ideal, we obtain the quotient of two subobjects and prove that the intersection of finite ideals is also an ideal in this category.

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24

Senapati, Tapan, Young Bae Jun, G. Muhiuddin, and K. P. Shum. "Cubic Intuitionistic Structures Applied to Ideals of BCI-Algebras." Analele Universitatii "Ovidius" Constanta - Seria Matematica 27, no. 2 (2019): 213–32. http://dx.doi.org/10.2478/auom-2019-0028.

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AbstractIn this paper, the notion of closed cubic intuitionistic ideals, cubic intuitionistic p-ideals and cubic intuitionistic a-ideals in BCI-algebras are introduced, and several related properties are investigated. Relations between cubic intuitionistic subalgebras, closed cubic intuitionistic ideals, cubic intuitionistic q-ideals, cubic intuitionistic p-ideals and cubic intuitionistic a-ideals are discussed. Conditions for a cubic intuitionistic ideal to be a cubic intuitionistic p-ideal are provided. Characterizations of a cubic intuitionistic a-ideal are considered. The cubic intuitionistic extension property for a cubic intuitionistic a-ideal is established.

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25

Feng, Yuming, та P. Corsini. "(λ,μ)-Fuzzy Version of Ideals, Interior Ideals, Quasi-Ideals, and Bi-Ideals". Journal of Applied Mathematics 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/425890.

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We introduced(λ,μ)-fuzzy ideals,(λ,μ)-fuzzy interior ideals,(λ,μ)-fuzzy quasi-ideals, and(λ,μ)-fuzzy bi-ideals of an ordered semigroup and studied them. Whenλ=0andμ=1, we meet the ordinary fuzzy ones. This paper can be seen as a generalization of Kehayopulu and Tsingelis (2006), Kehayopulu and Tsingelis (2007), and Yao (2009).

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26

Suriyakala, S., and R. Vembu. "Operations on ideals and corresponding ideal topologies." Novi Sad Journal of Mathematics 45, no. 2 (2015): 39–46. http://dx.doi.org/10.30755/nsjom.2014.013.

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27

Allen, Anita L. "IDEAS AND IDEALS: HONOURING JOYCE MITCHELL COOK." Think 20, no. 59 (2021): 31–47. http://dx.doi.org/10.1017/s1477175621000178.

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In the twentieth century, most PhD-trained academic philosophers in both the United States and United Kingdom were white men. The first black woman to earn a PhD in Philosophy was Joyce E. Mitchell Cook (1933–2014). A preacher's daughter from a small town in western Pennsylvania, Cook earned a BA from Bryn Mawr College. She went on to earn degrees in Psychology, Philosophy and Physiology from St Hilda's College at Oxford University before earning a PhD in Philosophy from Yale University in 1965. At Yale she served as Managing Editor of the Review of Metaphysics and was the first woman appointed as a teaching assistant in Philosophy. She taught at Howard University for nearly a decade and held positions in national government service in Washington, DC, before retiring to a life of independent study of the black experience. Although she did not publish much in her lifetime, Cook deserves to be remembered as: first, an academic trailblazer who proved that race and gender are not barriers to excellence in philosophy; second, a public philosopher who broke barriers as a foreign and economic affairs analyst and presidential speech writer; third, among the first philosophical bioethicists of informed consent and experimentation on humans; and, fourth, an analytic philosopher of race, opposing claims that blacks suffer from inherited intellectual inferiority. Cook's achievements can inspire women of all backgrounds who love philosophy to pursue graduate studies and academic careers.

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28

Albeverio, S., and V. Polischook. "Prüfer’s ideal numbers as Gelfand’s maximal ideals." P-Adic Numbers, Ultrametric Analysis, and Applications 2, no. 1 (2010): 35–54. http://dx.doi.org/10.1134/s2070046610010036.

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29

Rasouli, Saeed. "Rough ideals based on ideal determined varieties." Algebraic structures and their applications 6, no. 1 (2019): 1–21. http://dx.doi.org/10.29252/asta.6.1.1.

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30

Ohnishi, Satoshi, and Kei-ichi Watanabe. "Coefficient Ideal of Ideals Generated by Monomials." Communications in Algebra 39, no. 5 (2011): 1563–76. http://dx.doi.org/10.1080/00927871003639337.

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31

Abbasov, Abulhasan. "National ideology: conditions-requirements, ideas-ideals, principles." Journal of Problems of Eastern Philosophy, no. 30 (2024): 18. http://dx.doi.org/10.59849/2219-7370.2024.30.18.

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32

Shi, Jie Qiong, and Xiao Long Xin. "Ideal theory on EQ-algebras." AIMS Mathematics 6, no. 11 (2021): 11686–707. http://dx.doi.org/10.3934/math.2021679.

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<abstract><p>In this article, we introduce ideals and other special ideals on EQ-algebras, such as implicative ideals, primary ideals, prime ideals and maximal ideals. At first, we give the notion of ideal and its related properties on EQ-algebras, and give its equivalent characterizations. We discuss the relations between ideals and filters, and study the generating formula of ideals on EQ-algebras. Moreover, we study the properties of implicative ideals, primary ideals, prime ideals and maximal ideals and their relations. For example, we prove that every maximal ideal is prime and if prime ideals are implicative, then they are maximal in the EQ-algebra with the condition $ (DNP) $. Finally, we introduce the topological properties of prime ideals. We get that the set of all prime ideals is a compact $ T_{0} $ topological space. Also, we transferred the spectrum of EQ-algebras to bounded distributive lattices and given the ideal reticulation of EQ-algebras.</p></abstract>

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33

Rajaee, Saeed, Mehrdad Nasernejad, and Ibrahim Al-Ayyoub. "Superficial ideals for monomial ideals." Journal of Algebra and Its Applications 17, no. 06 (2018): 1850102. http://dx.doi.org/10.1142/s0219498818501025.

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Let [Formula: see text] and [Formula: see text] be two ideals in a commutative Noetherian ring [Formula: see text]. We say that [Formula: see text] is a superficial ideal for [Formula: see text] if the following conditions are satisfied: (i) [Formula: see text], where [Formula: see text] denotes a minimal set of generators of an ideal [Formula: see text]. (ii) [Formula: see text] for all positive integers [Formula: see text]. In this paper, by using some monomial operators, we first introduce several methods for constructing new ideals which have superficial ideals. In the sequel, we present some examples of monomial ideals which have superficial ideals. Next, we discuss on the relation between superficiality and normality. Finally, we explore the relation between normally torsion-freeness and superficiality.

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34

Han, Song-Chol. "Maximal k-ideals and r-ideals in semirings." Journal of Algebra and Its Applications 14, no. 10 (2015): 1250195. http://dx.doi.org/10.1142/s0219498812501952.

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Some properties of (left) k-ideals and r-ideals of a semiring are considered by the help of the congruence class semiring. It is proved that a proper k-ideal of a semiring with an identity is prime if it is a maximal left k-ideal. An equivalent condition for a proper r-ideal of a semiring being a maximal (left) r-ideal is established. It is shown that (left) r-ideals and (left) k-ideals coincide for an additively idempotent semiring, though the former is a special kind of the latter in general. It is proved that a proper k-ideal of an incline with an identity is a maximal k-ideal if and only if the corresponding congruence class semiring is the Boolean semiring.

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35

Ghlaim, Fatima M., and Fatema F. Kareem. "Cubic Ideals of TM-algebras." Ibn AL-Haitham Journal For Pure and Applied Sciences 36, no. 1 (2023): 367–79. http://dx.doi.org/10.30526/36.1.2920.

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For the generality of fuzzy ideals in TM-algebra, a cubic ideal in this algebra has been studied, such as cubic ideals and cubic T-ideals. Some properties of these ideals are investigated. Also, we show that the cubic T-ideal is a cubic ideal, but the converse is not generally valid. In addition, a cubic sub-algebra is defined, and new relations between the level subset and a cubic sub-algebra are discussed. After that, cubic ideals and cubic T-ideals under homomorphism are studied, and the image (pre-image) of cubic T-ideals is discussed. Finally, the Cartesian product of cubic ideals in Cartesian product TM-algebras is given. We proved that the product of two cubic ideals of the Cartesian product of two TM-algebras is also a cubic ideal.

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36

Khamrot, Pannawit, and Thiti Gaketem. "Application of Bipolar Fuzzy Set to a Novel of Fuzzy Ideal in $\Gamma$-Semigroups." European Journal of Pure and Applied Mathematics 16, no. 3 (2023): 1592–607. http://dx.doi.org/10.29020/nybg.ejpam.v16i3.4788.

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In this paper we define new types of bipolar fuzzy ideals, bipolar fuzzy almost ideals in $\Gamma$-semigroups. We discussed properties of bipolar fuzzy ideals, bipolar fuzzy almost ideals, minimal bipolar fuzzy ideal, minimal bipolar almost ideal in $\Gamma$-semigroups. Moreover, we prove connection between almost ideals and bipolar fuzzy almost ideals of $\Gamma$-semigroups.

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37

Liu, Yan, and Mucong Zheng. "Characterizations of Fuzzy Ideals in Coresiduated Lattices." Advances in Mathematical Physics 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/6423735.

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The notions of fuzzy ideals are introduced in coresiduated lattices. The characterizations of fuzzy ideals, fuzzy prime ideals, and fuzzy strong prime ideals in coresiduated lattices are investigated and the relations between ideals and fuzzy ideals are established. Moreover, the equivalence of fuzzy prime ideals and fuzzy strong prime ideals is proved in prelinear coresiduated lattices. Furthermore, the conditions under which a fuzzy prime ideal is derived from a fuzzy ideal are presented in prelinear coresiduated lattices.

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38

Li, Xiaowen, and Liyi Jia. "The Study and Investigation for the Ideals of New Generation Migrant Workers." Journal of Educational Theory and Management 2, no. 3 (2018): 76. http://dx.doi.org/10.26549/jetm.v2i3.991.

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(1) Objective: The study is to understand the overall situation of the ideas of new generation migrant workers and its influencing factors, so as to provide basis for the formulation of relevant countermeasures. (2) Methods: The article uses a self-made questionnaire for 613 new generation migrant workers to conduct a questionnaire investigation and statistical analysis of the results. (3) Results: The scores of the new generation migrant workers’ ideals from the highest to the lowest are life ideal, occupation ideal, physical ideal, development ideal and material ideal and the ideals have differences in gender, age, marital status and family residence. (4) Conclusion: The ideal levels are different and basically in the upper middle level.

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39

Börjesson, Lisa. "Beyond information policy." Journal of Documentation 72, no. 4 (2016): 674–95. http://dx.doi.org/10.1108/jdoc-10-2015-0134.

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Purpose – The purpose of this paper is to explore and explicate documentation ideals parallel to information policy, and by means of this analysis demonstrate how the concept “documentation ideals” is an analytical tool for engaging with political and institutional contexts of information practices. Design/methodology/approach – The paper is based on a case study of documentation ideals in a debate about quality in archaeological documentation. The methodology draws on idea analysis, and on the science and technology studies’ controversy studies approach. Findings – The paper explicates three documentation ideals, how these ideals allocate responsibility for documentation to different actors, how the ideals assign roles to practitioners, and how the ideals point to different beneficiaries of the documentation. Furthermore, the analysis highlights ideas about two different means to reach the documentation ideals. Research limitations/implications – The case’s debate reflects opinions of Northern European professionals. Social implications – The paper illuminates how documentation ideals tweak and even contest formal information policy in claims on the documentation and on the practitioners doing documentation. Originality/value – Documentation ideal analysis is crucial as a complement to formal information policy analysis and to analysis guided by practice theory in attempts to understand the contexts of information practices and documentation, insights central for developing information literacies.

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40

Long, Colby. "Initial ideals of Pfaffian ideals." Journal of Commutative Algebra 12, no. 1 (2020): 91–105. http://dx.doi.org/10.1216/jca.2020.12.91.

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41

Howald, J. A. "Multiplier ideals of monomial ideals." Transactions of the American Mathematical Society 353, no. 7 (2001): 2665–71. http://dx.doi.org/10.1090/s0002-9947-01-02720-9.

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42

Moghe, Sunishtha, and Niti Nipuna Saxena. "Idea of Victim Participation and Ideals of Sentencing." International Journal of Science and Research (IJSR) 14, no. 5 (2025): 176–81. https://doi.org/10.21275/sr25502090545.

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43

Palanikumar, M., and K. Arulmozhi. "ON NEW WAYS OF VARIOUS IDEALS IN TERNARY SEMIGROUPS." Matrix Science Mathematic 4, no. 1 (2020): 06–09. http://dx.doi.org/10.26480/msmk.01.2020.06.09.

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We discuss tri-quasi ideals and bi-quasi ideals in ternary semigroups and give some characterizations. The intersection of left, lateral and right ideals is a tri-ideal and product of left, lateral and right ideals is again a tri-ideal. We also discuss m-tri-ideals towards some characterizations in terms of tri-ideals. Some relevant counter examples are also indicated.

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44

ANDERSON, D. D., and JOHN KINTZINGER. "IDEALS IN DIRECT PRODUCTS OF COMMUTATIVE RINGS." Bulletin of the Australian Mathematical Society 77, no. 3 (2008): 477–83. http://dx.doi.org/10.1017/s0004972708000415.

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AbstractLet R and S be commutative rings, not necessarily with identity. We investigate the ideals, prime ideals, radical ideals, primary ideals, and maximal ideals of R×S. Unlike the case where R and S have an identity, an ideal (or primary ideal, or maximal ideal) of R×S need not be a ‘subproduct’ I×J of ideals. We show that for a ring R, for each commutative ring S every ideal (or primary ideal, or maximal ideal) is a subproduct if and only if R is an e-ring (that is, for r∈R, there exists er∈R with err=r) (or u-ring (that is, for each proper ideal A of R, $\sqrt {A}\not =R$)), the Abelian group (R/R2 ,+) has no maximal subgroups).

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Miccoli, Maria Maddalena, and Bedřich Pondělíček. "On $\alpha$-ideals and generalized $\alpha$-ideals in semigroups." Czechoslovak Mathematical Journal 39, no. 3 (1989): 522–27. http://dx.doi.org/10.21136/cmj.1989.102324.

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Dube, Themba, and Oghenetega Ighedo. "More ring-theoretic characterizations of P-frames." Journal of Algebra and Its Applications 14, no. 05 (2015): 1550061. http://dx.doi.org/10.1142/s0219498815500619.

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Call a ring z-good if it has the property that an ideal in it is a z-ideal if and only if its radical is a z-ideal. By first showing that a z-good ring is von Neumann regular if and only if every prime ideal in it is a z-ideal, we are able to characterize P-frames as precisely those L for which every prime ideal in the ring [Formula: see text] is a z-ideal. Furthermore, we show that this characterization still holds if prime ideals are replaced by essential ideals, radical ideals, convex ideals, or absolutely convex ideals.

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Jureczko, Joanna. "The new operations on complete ideals." Open Mathematics 17, no. 1 (2019): 415–22. http://dx.doi.org/10.1515/math-2019-0032.

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Abstract We introduce the notion of K-ideals associated with Kuratowski partitions. Using new operations on complete ideals we show connections between K-ideals and precipitous ideals and prove that every complete ideal can be represented by some K-ideal.

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48

Bedrood, Mahta, Farhad Sajadian, and Arsham Saeid. "Z◦−ideals in MV−algebras of continuous functions." Filomat 36, no. 7 (2022): 2439–50. http://dx.doi.org/10.2298/fil2207439b.

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In this paper, we study MV?algebra of continuous functions C(X) and maximal ideals of C(X). Furthermore, Z?ideal and Z??ideal of C(X) are introduced and proved that every Z??ideal in C(X) is a Z?ideal but the converse is not true and every finitely generated Z?ideal is a basic Z??ideal. Also, we investigate meet and join of two Z?ideals (Z??ideal) of C(X). Complemented elements of C(X) are examined and their properties have been studied. In particular, the relationship between generated ideal by them and Z?ideals (Z??ideals) is proved. Finally, we investigate some property of Z??ideals in basically disconnected space and extremally disconnected space.

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Jaber, Ameer. "Properties of ϕ-δ-primary and 2-absorbing δ-primary ideals of commutative rings". Asian-European Journal of Mathematics 13, № 01 (2018): 2050026. http://dx.doi.org/10.1142/s1793557120500266.

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Let [Formula: see text] be a commutative ring with unity [Formula: see text] and let [Formula: see text] be an ideal expansion. In the first part of this paper, we extend the concept of [Formula: see text]-primary ideals to [Formula: see text]-[Formula: see text]-primary ideals, where [Formula: see text] is an ideal reduction and [Formula: see text] is an ideal expansion. We introduce some of the ideal expansion [Formula: see text] and define [Formula: see text]-[Formula: see text]-primary ideals, where [Formula: see text] is an ideal reduction. Also, we investigate ideal expansions satisfying some additional conditions and prove more properties of the generalized [Formula: see text]-[Formula: see text]-primary ideals with respect to such an ideal expansion [Formula: see text]. In the second part of this paper we investigate 2-absorbing [Formula: see text]-primary ideals which unify 2-absorbing ideals and 2-absorbing primary ideals, where [Formula: see text] is an ideal expansion. A number of results in the two parts are given.

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Meng, Biao Long, and Xiao Long Xin. "On Fuzzy Ideals ofBL-Algebras." Scientific World Journal 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/757382.

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In this paper we investigate further properties of fuzzy ideals of aBL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of aBL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal may not be a fuzzy irreducible ideal and prove that a fuzzy prime idealωis a fuzzy irreducible ideal if and only ifω0=1and|Im⁡(ω)|=2. We give the Krull-Stone representation theorem of fuzzy ideals inBL-algebras. Furthermore, we prove that the lattice of all fuzzy ideals of aBL-algebra is a complete distributive lattice. Finally, it is proved that every fuzzy Boolean ideal is a fuzzy Gödel ideal, but the converse implication is not true.

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