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Journal articles on the topic 'Near-rings'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

C, Dhivya, and Radha D. "Semimedial Near Rings." Indian Journal Of Science And Technology 17, no. 24 (2024): 2478–81. http://dx.doi.org/10.17485/ijst/v17i24.1403.

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Objectives: To define the term ‘semimediality’ in the near ring and to demonstrate its presence with an example and to employ several attributes in near rings to analyse its features. Methods: Semimedial near rings are examined in terms of their characteristics using commutativity, distributivity and regular property. The distinction is observed using the concept of homomorphism. Findings: Every near ring which is weak commutative is proved to be semimedial and the converse exists with some additional axioms. The semimedial near ring’s anti-homomorphic image is also observed. Additionally, the

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2

Valli, S. R. Veronica, та K. Bala Deepa Arasi. "ஜ ஜ Near Semi Rings". Indian Journal Of Science And Technology 17, № 26 (2024): 2679–82. http://dx.doi.org/10.17485/ijst/v17i26.1524.

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Objectives: In the widened area of near semi rings, this article speaks about the interventions of a specific sub structure. Methods: Heading towards a more unique functionality, the chosen sub structure is intervened with regularity, homomorphism and also checked for weak commutative idempotency. Findings: The desired sub-structure is descried to have been preserved under homomorphism and is also found to be isomorphic to sub direct products of sub-directly irreducible sub structures. Novelty: Few descriptions and differences on weak commutative regularity and regular idempotency has been exp

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3

Smith, Kirby C., and Leon Wyk. "Matrix Near-rings over Centralizer Near-rings." Algebra Colloquium 7, no. 1 (2000): 5–16. http://dx.doi.org/10.1007/s10011-000-0005-5.

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4

Meldrum, J. D. P. "NEAR-RINGS." Bulletin of the London Mathematical Society 27, no. 4 (1995): 405–6. http://dx.doi.org/10.1112/blms/27.4.405.

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5

Booth, G. L., та S. Veldsman. "Special radicals of near-rings and Γ-near-rings". Periodica Mathematica Hungarica 29, № 2 (1994): 111–26. http://dx.doi.org/10.1007/bf01876869.

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6

Cho, Yong Uk. "NEW KINDS OF NEAR-RINGS FROM OLD NEAR RINGS." JP Journal of Algebra, Number Theory and Applications 40, no. 3 (2018): 255–61. http://dx.doi.org/10.17654/nt040030255.

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7

Islam, Md Rezaul, and Satrajit Kumar Saha. "Endomorphism Rings are Centralizer Near-rings." GANIT: Journal of Bangladesh Mathematical Society 34 (June 28, 2016): 57–61. http://dx.doi.org/10.3329/ganit.v34i0.28554.

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For a finite ring R with identity and a finite unital R-module V the set C(R; V) = {f : V ->V : f(?v) = ?f(v) for all ? ? R, v ? V} is the centralizer near-ring determined by R and V. Rings R for witch C(R; V) is a ring for every R-module V, are characterized. Conditions are given under which C(R; V) is a semisimple centralizer near ring. Its shown that C(R; V) is a semisimple centralizer near ring then EndR(V) = C(R; V).GANIT J. Bangladesh Math. Soc.Vol. 34 (2014) 57-61

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8

Ham, Kyung-Yuen, Young-Cheol Jeon, Jin-Woo Kang, et al. "IFP RINGS AND NEAR-IFP RINGS." Journal of the Korean Mathematical Society 45, no. 3 (2008): 727–40. http://dx.doi.org/10.4134/jkms.2008.45.3.727.

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9

Hausen, Jutta, and Johnny A. Johnson. "Centralizer near-rings that are rings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 59, no. 2 (1995): 173–83. http://dx.doi.org/10.1017/s144678870003857x.

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AbstractGiven an R-module M, the centralizer near-ring ℳR (M) is the set of all functions f: M → M with f(xr)= f(x)r for all x ∈ M and r∈R endowed with point-wise addition and composition of functions as multiplication. In general, ℳR(M) is not a ring but is a near-ring containing the endomorphism ring ER(M) of M. Necessary and/or sufficient conditions are derived for ℳR(M) to be a ring. For the case that R is a Dedekind domain, the R-modules M are characterized for which (i) ℳR(M) is a ring; and (ii)ℳR(M) = ER(M). It is shown that over Dedekind domains with finite prime spectrum properties (i

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10

Bell, Howard E. "Certain near-rings are rings, II." International Journal of Mathematics and Mathematical Sciences 9, no. 2 (1986): 267–72. http://dx.doi.org/10.1155/s0161171286000327.

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We investigate distributively-generated near-ringsRwhich satisfy one of the following conditions: (i) for eachx,y∈R, there exist positive integersm,nfor whichxy=ymxn; (ii) for eachx,y∈R, there exists a positive integernsuch thatxy=(yx)n. Under appropriate additional hypotheses, we prove thatRmust be a commutative ring.

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11

De Stefano, Stefania, and Simonetta Di Sieno. "Semiprime near-rings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 51, no. 1 (1991): 88–94. http://dx.doi.org/10.1017/s1446788700033322.

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12

Kyuno, Shoji, and Stefan Veldsman. "MORITA NEAR-RINGS." Quaestiones Mathematicae 15, no. 4 (1992): 431–49. http://dx.doi.org/10.1080/16073606.1992.9631703.

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13

Dumitru, Mariana, Laura Năstăsescu, and Bogdan Toader. "Graded near-rings." Analele Universitatii "Ovidius" Constanta - Seria Matematica 24, no. 1 (2016): 201–16. http://dx.doi.org/10.1515/auom-2016-0011.

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AbstractIn this paper, we consider graded near-rings over a monoid G as generalizations of graded rings over groups, and study some of their basic properties. We give some examples of graded near-rings having various interesting properties, and we define and study the Gop-graded ring associated to a G-graded abelian near-ring, where G is a left cancellative monoid and Gop is its opposite monoid. We also compute the graded ring associated to the graded near-ring of polynomials (over a commutative ring R) whose constant term is zero.

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14

Sugantha, G., and R. Balakrishnan. "\beta_1 near-rings." International Journal of Algebra 8 (2014): 1–7. http://dx.doi.org/10.12988/ija.2014.311127.

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15

Chatters, A. W. "Near-dedekind rings." Communications in Algebra 28, no. 4 (2000): 1957–70. http://dx.doi.org/10.1080/00927870008826938.

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16

Feigelstock, S. "E -near rings." Archiv der Mathematik 78, no. 2 (2002): 124–25. http://dx.doi.org/10.1007/s00013-002-8225-1.

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17

Meldrum, J. D. P., and A. P. J. van der Walt. "Matrix near-rings." Archiv der Mathematik 47, no. 4 (1986): 312–19. http://dx.doi.org/10.1007/bf01191356.

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18

Birkenmeier, Gary, and Henry Heatherly. "Medial near-rings." Monatshefte f�r Mathematik 107, no. 2 (1989): 89–110. http://dx.doi.org/10.1007/bf01300916.

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19

Dhivya, C., and D. Radha. "Semimedial Near Rings." Indian Journal of Science and Technology 17, no. 24 (2024): 2478–81. https://doi.org/10.17485/IJST/v17i24.1403.

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Abstract <strong>Objectives:</strong> To define the term ‘semimediality’ in the near ring and to demonstrate its presence with an example and to employ several attributes in near rings to analyse its features. <strong>Methods:</strong> Semimedial near rings are examined in terms of their characteristics using commutativity, distributivity and regular property. The distinction is observed using the concept of homomorphism. <strong>Findings:</strong> Every near ring which is weak commutative is proved to be semimedial and the converse exists with some additio

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20

Smith, Kirby C., and Leon van Wyk. "Centralizer Near-rings, Matrix Near-rings and Cyclic p-Groups." Algebra Colloquium 12, no. 04 (2005): 567–84. http://dx.doi.org/10.1142/s1005386705000532.

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If G is a finite group and [Formula: see text] is a group of automorphisms of G, then it is known that the matrix near-ring [Formula: see text] is a subnear-ring of the centralizer near-ring [Formula: see text] for every m ≥ 2. Conditions are known under which [Formula: see text] is a proper subnear-ring of [Formula: see text], and if [Formula: see text] and G are abelian, then conditions are known which imply the equality [Formula: see text]. In this paper, we characterize the groups [Formula: see text] of automorphisms of a cyclic p-group G for which this equality holds. We also show that fo

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21

Wendt, Gerhard. "$0$-PRIMITIVE NEAR-RINGS, MINIMAL IDEALS AND SIMPLE NEAR-RINGS." Taiwanese Journal of Mathematics 19, no. 3 (2015): 875–905. http://dx.doi.org/10.11650/tjm.19.2015.5077.

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22

Raji, A. "Some commutativity criteria for 3-prime near-rings." Algebra and Discrete Mathematics 32, no. 2 (2021): 280–98. http://dx.doi.org/10.12958/adm1439.

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In the present paper, we introduce the notion of∗-generalized derivation in near-ring N and investigate some properties in volving that of∗-generalized derivation of a∗-prime near-ring N which forces N to be a commutative ring. Some properties of generalized semiderivations have also been given in the context of 3-prime near-rings. Consequently, some well known results have beengeneralized. Furthermore, we will give examples to demonstratethat the restrictions imposed on the hypothesis of various resultsare not superŕuous.

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23

Sezgin, Aslıhan, Osman Atagün, and Emin Aygün. "A note on soft near-rings and idealistic soft near-rings." Filomat 25, no. 1 (2011): 53–68. http://dx.doi.org/10.2298/fil1101053s.

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Molodtsov introduced the theory of soft sets, which can be seen as an effective mathematical tool to deal with uncertainties, since it is free from the difficulties that the usual theoretical approaches have troubled. In this paper, we apply the definitions proposed by Ali et al. [M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57 (2009), 1547-1553] to the concept of soft near- rings and substructures of soft near-rings, proposed by Atag?n and Sezgin [A. O. Atag?n and A. Sezgin, Soft Near-rings, submitted] and show them with i

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24

Heatherly, H., and G. Pilz. "On the structure of tame near-rings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 50, no. 2 (1991): 316–19. http://dx.doi.org/10.1017/s1446788700032778.

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AbstractTame near-rings form an important class of near-rings. They have the common feature that all N-subgroups in a faithful N-group are ideals. Tame near-rings can be very close to and very far from rings. Most of the important classes of distributively generated near-rings and all 2-semisimple near-rings are examples of tame near-rings.

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25

AKIN, OSMAN ATAG\"{U}N, and SEZGİN ASLIHAN. "From a different point of view to near-rings: Soft zero-symmetric and constant parts of soft near-rings with applications." Asia Mathematika 8, no. 1 (2024): 58——73. https://doi.org/10.5281/zenodo.12966270.

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In this study, we describe soft parts, named soft 0-symmetric and soft constant parts, of soft intersection near-rings and soft union near-rings, and obtain their fundamental features. We explore the relations between the parts of near-rings and soft parts of soft intersection near-rings and soft union near-rings, and we give some applications of these parts to soft sets. Additionally, soft intersection (union) product of soft intersection (union) near-ring are introduced and applied on soft parts of soft intersection near-rings and soft union near-rings, respectively.

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26

TRIWULANDARI, PRADITA Z., KARTIKA SARI, and LUH PUTU IDA HARINI. "HUBUNGAN DERIVASI PRIME NEAR-RING DENGAN SIFAT KOMUTATIF RING." E-Jurnal Matematika 6, no. 2 (2017): 116. http://dx.doi.org/10.24843/mtk.2017.v06.i02.p155.

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Near-rings are generalize from rings. A research on near-ring is continous included a research on prime near-rings and one of this research is about derivation on prime near-rings. This article will reviewing about relation between derivation on prime near-rings and commutativity in rings with literature review method. The result is prime near-rings are commutative rings if a nonzero derivation d on N hold one of this following conditions: (i) , (ii) , (iii) , (iv) , (v) , (vi) , for all , with is non zero semigroup ideal from .

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27

Tharmaratinam, V. "Matrix d.g. near-rings." Proceedings of the Edinburgh Mathematical Society 41, no. 3 (1998): 433–46. http://dx.doi.org/10.1017/s0013091500019817.

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Matrix near-rings had been defined by Meldrum and Van der Walt in 1986 and although a fair amount of results on the structure of these near-rings have been obtained since then, a satisfactory structure theory has yet to be developed for matrix d.g. near-rings. In this paper we give an alternate definition (in fact the dual definition) for matrix d.g. near-rings and develop a satisfactory structure theory for such d.g. near-rings.

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28

Hoskova-Mayerova, Sarka, and Madeline Al Tahan. "Anti-Fuzzy Multi-Ideals of Near Ring." Mathematics 9, no. 5 (2021): 494. http://dx.doi.org/10.3390/math9050494.

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Recently, fuzzy multisets have come to the forefront of scientists’ interest and have been used for algebraic structures such as groups, rings, and near rings. In this paper, we first summarize the knowledge about algebraic structure of fuzzy multisets such as fuzzy multi-subnear rings and fuzzy multi-ideals of near rings. Then we recall the results from our related previous work, where we defined different operations on fuzzy multi-ideals of near rings and we generalized some known results for fuzzy ideals of near rings to fuzzy multi-ideals of near rings. Finally, we define anti-fuzzy multi-

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29

Yakabe, Iwao. "Regular duo near-rings." Proceedings of the Japan Academy, Series A, Mathematical Sciences 66, no. 5 (1990): 115–18. http://dx.doi.org/10.3792/pjaa.66.115.

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30

ÇOKAKOĞLU, Baki, and Mustafa UÇKUN. "Nearness Gamma-Near Rings." Fundamentals of Contemporary Mathematical Sciences 3, no. 1 (2022): 46–56. http://dx.doi.org/10.54974/fcmathsci.1032011.

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31

Leerawat, Utsanee, Monrudee Sirivoravit, and Katthaleeya Daowsud. "On near generalized rings." Journal of Discrete Mathematical Sciences and Cryptography 23, no. 5 (2020): 1085–99. http://dx.doi.org/10.1080/09720529.2020.1750104.

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32

Booth, G. L., та N. J. Groenewald. "EQUIPRIME Γ-NEAR-RINGS". Quaestiones Mathematicae 14, № 4 (1991): 411–17. http://dx.doi.org/10.1080/16073606.1991.9631659.

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33

Booth, G. L., N. J. Groenewald, and S. Veldsman. "STRONGLY EQUIPRIME NEAR-RINGS." Quaestiones Mathematicae 14, no. 4 (1991): 483–89. http://dx.doi.org/10.1080/16073606.1991.9631665.

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34

Smith, Kirby C. "Generalized matrix near-rings." Communications in Algebra 24, no. 6 (1996): 2065–77. http://dx.doi.org/10.1080/00927879608825688.

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35

Syskin, Sergei A. "Isomorphic endomorphism near-rings." Communications in Algebra 26, no. 8 (1998): 2429–34. http://dx.doi.org/10.1080/00927879808826287.

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36

Boykett, Tim, and Gerhard Wendt. "Units in Near-Rings." Communications in Algebra 44, no. 4 (2016): 1478–95. http://dx.doi.org/10.1080/00927872.2015.1012674.

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37

Groenewald, N. J. "Strongly prime near-rings." Proceedings of the Edinburgh Mathematical Society 31, no. 3 (1988): 337–43. http://dx.doi.org/10.1017/s0013091500006738.

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Strongly prime rings were introduced by Handelman and Lawrence [5] and in [2] Groenewald and Heyman investigated the upper radical determined by the class of all strongly prime rings. In this paper we extend the concept of strongly prime to near-rings. We show that the class M of distributively generated near-rings is a special class in the sense of Kaarli [6]. We also show that if N is any distributively generated near-ring, then UM(N), UM denotes the upper radical determined by the class M, coincides with the intersection of all the strongly prime ideals of N.

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38

Lyons, Carter G., and Gary L. Peterson. "Local endomorphism near-rings." Proceedings of the Edinburgh Mathematical Society 31, no. 3 (1988): 409–14. http://dx.doi.org/10.1017/s0013091500006805.

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The purpose of this paper is to study the consequences of an endomorphism near-ring of a finite group being a local near-ring and the existence of such near-rings. As we shall see in Section 2, an endomorphism near-ring of a finite group being local gives us some information about both the structure of the group (Theorem 2.2) and the automorphisms of the group lying in the near-ring (Theorem 2.3). Existence of local endomorphism near-rings of finite groups is considered in Section 3 where we obtain as our main result that any p-group of automorphisms of a p-group containing the inner automorph

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39

Jones, Patricia. "Zero square near-rings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 51, no. 3 (1991): 497–504. http://dx.doi.org/10.1017/s1446788700034662.

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AbstractThe purpose of this paper is to provide examples and explore properties of a wide variety of zero square (left) near rings. Among the main results are complete classifications of (i) finite Abelian groups which are the additive group of a zero square near-ring and (ii) finite non-Abelian groups which support 3-nilpotent distributive zero square near-rings.

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40

Maxson, C. J., and L. van Wyk. "Near-Rings of Invariants." Results in Mathematics 18, no. 3-4 (1990): 286–97. http://dx.doi.org/10.1007/bf03323173.

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41

Zayed, M. "On matrix near-rings." Archiv der Mathematik 77, no. 2 (2001): 163–69. http://dx.doi.org/10.1007/pl00000476.

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42

Franetič, Damir. "Local loop near-rings." Rendiconti del Seminario Matematico della Università di Padova 138 (December 22, 2017): 223–37. http://dx.doi.org/10.4171/rsmup/138-11.

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43

Peterson, Gary L. "Weakly tame near-rings." Communications in Algebra 19, no. 4 (1991): 1165–81. http://dx.doi.org/10.1080/00927879108824196.

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44

Veldsman, Stefan. "On equiprime near-rings." Communications in Algebra 20, no. 9 (1992): 2569–87. http://dx.doi.org/10.1080/00927879208824479.

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45

Scapellato, Raffaele. "Strongly monogenic near-rings." Archiv der Mathematik 51, no. 5 (1988): 476–80. http://dx.doi.org/10.1007/bf01198634.

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46

le Riche, L. R., J. D. P. Meldrum, and A. P. J. van der Walt. "On group near-rings." Archiv der Mathematik 52, no. 2 (1989): 132–39. http://dx.doi.org/10.1007/bf01191265.

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47

van der Walt, Andries P. J. "Matrix near-rings contained in 2-primitive near-rings with minimal subgroups." Journal of Algebra 148, no. 2 (1992): 296–304. http://dx.doi.org/10.1016/0021-8693(92)90195-r.

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48

Vineela Korada, V. P., S. Ragamayi, and Aiyared Iampan. "Bipolar Fuzzy Filters of Gamma-Near Rings." International Journal of Analysis and Applications 22 (January 3, 2024): 2. http://dx.doi.org/10.28924/2291-8639-22-2024-2.

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The main objective of this paper is to present the notation of bipolar fuzzy filters of Γ-near rings and ordered Γ-near rings. As a consequence, we deal with bipolar fuzzy prime ideals of Γ-near rings and ordered Γ-near rings. Also, we examine the one-to-one correspondence of bipolar fuzzy filters and crisp filters of Γ-near rings. Later, we define and study the homomorphism of ordered Γ-near rings.

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49

Ahsan, Javed, and Gordon Mason. "Fully idempotent near-rings and sheaf representations." International Journal of Mathematics and Mathematical Sciences 21, no. 1 (1998): 145–51. http://dx.doi.org/10.1155/s0161171298000192.

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Fully idempotent near-rings are defined and characterized which yields information on the lattice of ideals of fully idempotent rings and near-rings. The space of prime ideals is topologized and a sheaf representation is given for a class of fully idempotent near-rings which includes strongly regular near-rings.

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50

Quadri, Murtaza A., M. Ashraf, and Asma Ali. "Certain conditions under which near-rings are rings." Bulletin of the Australian Mathematical Society 42, no. 1 (1990): 91–94. http://dx.doi.org/10.1017/s0004972700028173.

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In 1969, Ligh proved that distributively generated (d-g) Boolean near-rings are rings, and hinted that some of the more complicated polynomial identities implying commutativity in rings may turn d-g near-rings into rings. In the present paper we investigate the following conditions: (1) xy = (xy)n(x, y); (2) xy = (yz)n (xy); (3) xy = ym (x, y)xn (x, y); (4) xy = xy n(x, y)x; (5) xy = xn(x, y)ym (x, y); finally prove that under appropriate additional hypotheses a d-g near-ring must be a commutative ring. Indeed the theorem proved here is a wide generalisation of many recently established result

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