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Journal articles on the topic 'Graded modules'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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1

Bataineh, Malik, Rashid Abu-Dawwas, and Jenan Shtayat. "Almost graded multiplication and almost graded comultiplication modules." Demonstratio Mathematica 53, no. 1 (December 31, 2020): 325–31. http://dx.doi.org/10.1515/dema-2020-0023.

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AbstractLet G be a group with identity e, R be a G-graded commutative ring with a nonzero unity 1 and M be a G-graded R-module. In this article, we introduce and study the concept of almost graded multiplication modules as a generalization of graded multiplication modules; a graded R-module M is said to be almost graded multiplication if whenever a\in h(R) satisfies {\text{Ann}}_{R}(aM)={\text{Ann}}_{R}(M), then (0{:}_{M}a)=\{0\}. Also, we introduce and study the concept of almost graded comultiplication modules as a generalization of graded comultiplication modules; a graded R-module M is said to be almost graded comultiplication if whenever a\in h(R) satisfies {\text{Ann}}_{R}(aM)={\text{Ann}}_{R}(M), then aM=M. We investigate several properties of these classes of graded modules.

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2

Bataineh, Malik, Rashid Abu-Dawwas, and Jenan Shtayat. "Almost graded multiplication and almost graded comultiplication modules." Demonstratio Mathematica 53, no. 1 (December 31, 2020): 325–31. http://dx.doi.org/10.1515/dema-2020-0023.

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AbstractLet G be a group with identity e, R be a G-graded commutative ring with a nonzero unity 1 and M be a G-graded R-module. In this article, we introduce and study the concept of almost graded multiplication modules as a generalization of graded multiplication modules; a graded R-module M is said to be almost graded multiplication if whenever a\in h(R) satisfies {\text{Ann}}_{R}(aM)={\text{Ann}}_{R}(M), then (0{:}_{M}a)=\{0\}. Also, we introduce and study the concept of almost graded comultiplication modules as a generalization of graded comultiplication modules; a graded R-module M is said to be almost graded comultiplication if whenever a\in h(R) satisfies {\text{Ann}}_{R}(aM)={\text{Ann}}_{R}(M), then aM=M. We investigate several properties of these classes of graded modules.

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3

Abu-Dawwas, Rashid. "Graded semiprime multiplication modules." Boletim da Sociedade Paranaense de Matemática 39, no. 3 (January 1, 2021): 27–35. http://dx.doi.org/10.5269/bspm.40197.

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Let $M$ be a $G$-graded $R$-module. In this article, we introduce the concept of graded semiprime multiplication modules. A graded $R$-module $M$ is said to be graded semiprime multiplication if $M$ has no graded semiprime $R$-submodules or for every graded semiprime $R$-submodule $N$ of $M$, $N=IM$ for some graded ideal $I$ of $R$. We introduce several results concerning graded semiprime submodules and we investigate them to present several results on graded semiprime multiplication modules.

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4

ZAMANI, NASER. "FINITELY GENERATED GRADED MULTIPLICATION MODULES." Glasgow Mathematical Journal 53, no. 3 (August 1, 2011): 693–705. http://dx.doi.org/10.1017/s0017089511000279.

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AbstractLet R = ⊕i ∈ ℤRi be a ℤ-graded ring and M = ⊕i ∈ ℤMi be a graded R-module. Providing some results on graded multiplication modules, some equivalent conditions for which a finitely generated graded R-module to be graded multiplication will be given. We define generalised graded multiplication module and determine some of its certain graded prime submodules. It will be shown that any graded submodule of a finitely generated generalised graded multiplication R-module M has a kind of primary decomposition. Using this, we give a characterisation of graded primary submodules of M. These lead to a kind of characterisation of finitely generated generalised graded multiplication modules.

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5

Al-Zoubi, Khaldoun falah, and Rweili Alkhalaf. "On graded quasi-primary submodules of graded modules over graded commutative rings." Boletim da Sociedade Paranaense de Matemática 39, no. 4 (January 1, 2021): 57–64. http://dx.doi.org/10.5269/bspm.41917.

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Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce the concept of graded quasi-primary submodules of graded modules over graded commutative rings. Various properties of graded quasi-primary submodules are considered.

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6

Khashyarmaneshs, Kazem, and Ahmad Abbasi. "On the asymptotic behaviour of associated primes of generalized local cohomology modules." Journal of the Australian Mathematical Society 83, no. 2 (October 2007): 217–26. http://dx.doi.org/10.1017/s1446788700036879.

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AbstractLetMandNbe finitely generated and graded modules over a standard positive graded commutative Noetherian ringR, with irrelevant idealR+. Letbe thenth component of the graded generalized local cohomology module. In this paper we study the asymptotic behavior of AssfR+() as n → –∞ wheneverkis the least integerjfor which the ordinary local cohomology moduleis not finitely generated.

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7

Khaksari, A., and F. Rasti Jahromi. "Multiplication graded modules." International Journal of Algebra 7 (2013): 17–24. http://dx.doi.org/10.12988/ija.2013.13003.

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8

Balaba, I. N. "Prime graded modules." Journal of Mathematical Sciences 163, no. 5 (November 14, 2009): 487–92. http://dx.doi.org/10.1007/s10958-009-9686-6.

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9

Ghiasvand, Peyman, and Farkhonde Farzalipour. "On graded weak multiplication modules." Tamkang Journal of Mathematics 43, no. 2 (June 30, 2012): 171–77. http://dx.doi.org/10.5556/j.tkjm.43.2012.712.

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10

Abrams, Gene, and Claudia Menini*. "EMBEDDING MODULES IN GRADED MODULES OVER A SEMIGROUP-GRADED RING." Communications in Algebra 29, no. 6 (April 30, 2001): 2611–25. http://dx.doi.org/10.1081/agb-100002411.

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11

Darani, Ahmad Yousefian. "GRADED PRIMAL SUBMODULES OF GRADED MODULES." Journal of the Korean Mathematical Society 48, no. 5 (September 1, 2011): 927–38. http://dx.doi.org/10.4134/jkms.2011.48.5.927.

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12

Al-Zoubi, Khaldoun, and Amani Al-Qderat. "Some properties of graded comultiplication modules." Open Mathematics 15, no. 1 (March 4, 2017): 187–92. http://dx.doi.org/10.1515/math-2017-0016.

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Abstract Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper we will obtain some results concerning the graded comultiplication modules over a commutative graded ring.

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13

Lin, Weiqiang, and Yucai Su. "Quasi-finite Irreducible Graded Modules for the Virasoro-like Algebra." Algebra Colloquium 20, no. 02 (April 3, 2013): 181–96. http://dx.doi.org/10.1142/s1005386713000175.

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In this paper, we consider the classification of irreducible Z- and Z2-graded modules with finite-dimensional homogeneous subspaces over the Virasoro-like algebra. We prove that such a module is a uniformly bounded module or a generalized highest weight module. Then we determine all generalized highest weight quasi-finite irreducible modules. As a consequence, we determine all the modules with nonzero center. Finally, we prove that there does not exist any non-trivial Z-graded module of intermediate series.

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14

Al-Zoubi, Khaldoun. "Some properties of graded 2-prime submodules." Asian-European Journal of Mathematics 08, no. 02 (June 2015): 1550016. http://dx.doi.org/10.1142/s1793557115500163.

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Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded 2-prime submodule and we give a number of results concerning such modules. Also, we introduce and prove the graded 2-prime avoidance theorem for graded modules.

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15

Wu, Yina, and Weiqiang Lin. "Classification of Z-Graded Modules of the Intermediate Series over the q-Analog Virasoro-like Algebra." Algebra Colloquium 17, no. 02 (June 2010): 247–56. http://dx.doi.org/10.1142/s100538671000026x.

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In this paper, we complete the classification of Z-graded modules of the intermediate series over a q-analog Virasoro-like algebra L. We first construct four classes of irreducible Z-graded L-modules of the intermediate series. Then we prove that any Z-graded L-module of the intermediate series must be one of the modules constructed by us, or a direct sum of some trivial L-modules.

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16

El Din S. Hussein, Salah. "Graded Essential Extensions and Graded Injective Modules." Pure and Applied Mathematics Journal 4, no. 2 (2015): 47. http://dx.doi.org/10.11648/j.pamj.20150402.13.

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17

Nhi, Dam Van. "SPECIALIZATION OF GRADED MODULES." Proceedings of the Edinburgh Mathematical Society 45, no. 2 (June 2002): 491–506. http://dx.doi.org/10.1017/s0013091500000602.

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AbstractThe paper shows that specializations of finitely generated graded modules are also graded and that many important invariants of graded modules and ideals are preserved by specializations.AMS 2000 Mathematics subject classification: Primary 13A02

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18

ABU-DAWWAS, Rashid, Malik BATAINEH, and Adeela DA'KEEK. "Graded weak comultiplication modules." Hokkaido Mathematical Journal 48, no. 2 (June 2019): 253–61. http://dx.doi.org/10.14492/hokmj/1562810507.

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19

Ansari-Toroghy, H., and F. Farshadifar. "On graded second modules." Tamkang Journal of Mathematics 43, no. 4 (December 31, 2012): 499–505. http://dx.doi.org/10.5556/j.tkjm.43.2012.1319.

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20

Webb, Cary. "Decomposition of graded modules." Proceedings of the American Mathematical Society 94, no. 4 (April 1, 1985): 565. http://dx.doi.org/10.1090/s0002-9939-1985-0792261-6.

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21

Wang, Chunxiang. "Graded Hilbert C*-modules." Journal of Mathematical Physics 55, no. 2 (February 2014): 023504. http://dx.doi.org/10.1063/1.4863902.

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22

Năstăsescu, C., S. Raianu, and F. Van Oystaeyen. "Modules graded byG-sets." Mathematische Zeitschrift 203, no. 1 (January 1990): 605–27. http://dx.doi.org/10.1007/bf02570759.

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23

He, JiWei, and QuanShui Wu. "Koszul differential graded modules." Science in China Series A: Mathematics 52, no. 9 (September 2009): 2027–35. http://dx.doi.org/10.1007/s11425-008-0169-x.

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24

Mao, Lixin. "Strongly Gorenstein graded modules." Frontiers of Mathematics in China 12, no. 1 (October 20, 2016): 157–76. http://dx.doi.org/10.1007/s11464-016-0595-y.

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25

Puspita, Nikken Prima, Indah Emilia Wijayanti, and Budi Surodjo. "Graded Modules as a Clean Comodule." Journal of Mathematics Research 12, no. 6 (November 11, 2020): 66. http://dx.doi.org/10.5539/jmr.v12n6p66.

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In ring and module theory, the cleanness property is well established. If any element of R can be expressed as the sum of an idempotent and a unit, then R is said to be a clean ring. Moreover, an R-module M is clean if the endomorphism ring of M is clean. We study the cleanness concept of coalgebra and comodules as a dualization of the cleanness in rings and modules. Let C be an R-coalgebra and M be a C-comodule. Since the endomorphism of C-comodule M is a ring, M is called a clean C-comodule if the ring of C-comodule endomorphisms of M is clean. In Brzezi´nski and Wisbauer (2003), the group ring R[G] is an R-coalgebra. Consider M as an R[G]-comodule. In this paper, we have investigated some sucient conditions to make M a clean R[G]-comodule, and have shown that every G-graded module M is a clean R[G]-comodule if M is a clean R-module.

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26

MAO, LIXIN. "DING-GRADED MODULES AND GORENSTEIN GR-FLAT MODULES." Glasgow Mathematical Journal 60, no. 2 (November 2, 2017): 339–60. http://dx.doi.org/10.1017/s0017089517000155.

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AbstractLet R be a graded ring. We introduce the concepts of Ding gr-injective and Ding gr-projective R-modules, which are the graded analogues of Ding injective and Ding projective modules. Several characterizations and properties of Ding gr-injective and Ding gr-projective modules are obtained. In addition, we investigate the relationships among Gorenstein gr-flat, Ding gr-injective and Ding gr-projective modules.

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27

Ooishi, Akira. "On the associated graded modules of canonical modules." Journal of Algebra 141, no. 1 (August 1991): 143–57. http://dx.doi.org/10.1016/0021-8693(91)90208-p.

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28

Hayasaka, Futoshi, and Eero Hyry. "A Family of Graded Modules Associated to a Module." Communications in Algebra 36, no. 11 (November 6, 2008): 4201–17. http://dx.doi.org/10.1080/00927870802177291.

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29

Yoshino, Yuji. "Graded CM modules over graded normal CM domains." Journal of Mathematics of Kyoto University 32, no. 1 (1992): 73–91. http://dx.doi.org/10.1215/kjm/1250519598.

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30

Hussien, Salah El Din S., Essam El-Seidy, and Manar E. Tabarak. "Graded injective modules and graded quasi-Frobenius rings." Applied Mathematical Sciences 9 (2015): 1113–23. http://dx.doi.org/10.12988/ams.2015.4121036.

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31

Tavallaee, Hamid Agha, and Masoud Zolfaghari. "Graded weakly semiprime submodules of graded multiplication modules." Lobachevskii Journal of Mathematics 34, no. 1 (January 2013): 61–67. http://dx.doi.org/10.1134/s1995080213010113.

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32

Auslander, Maurice, and Idun Reiten. "Graded modules and their completions." Banach Center Publications 26, no. 1 (1990): 181–92. http://dx.doi.org/10.4064/-26-1-181-192.

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33

Abu-Dawwas, Rashid, Khaldoun Al-Zoubi, and Malik Bataineh. "Prime Submodules of Graded Modules." Proyecciones (Antofagasta) 31, no. 4 (December 2012): 355–61. http://dx.doi.org/10.4067/s0716-09172012000400004.

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34

Gao, Zenghui, and Jie Peng. "$n$-strongly Gorenstein graded modules." Czechoslovak Mathematical Journal 69, no. 1 (May 21, 2018): 55–73. http://dx.doi.org/10.21136/cmj.2018.0160-17.

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35

Tang, Zhongming. "On certain graded artinian modules." Communications in Algebra 21, no. 1 (January 1993): 255–68. http://dx.doi.org/10.1080/00927879208824559.

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36

Rotthaus, Christel, and Liana M. Şega. "Open loci of graded modules." Transactions of the American Mathematical Society 358, no. 11 (April 11, 2006): 4959–80. http://dx.doi.org/10.1090/s0002-9947-06-03876-1.

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37

Hu, Jun, and Andrew Mathas. "Graded Induction for Specht Modules." International Mathematics Research Notices 2012, no. 6 (April 22, 2011): 1230–63. http://dx.doi.org/10.1093/imrn/rnr058.

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38

Chen, Justin, and Youngsu Kim. "Graded-irreducible modules are irreducible." Communications in Algebra 45, no. 5 (October 7, 2016): 1907–13. http://dx.doi.org/10.1080/00927872.2016.1226864.

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39

Kraft, Hanspeter, and Claudio Procesi. "Graded morphisms of $G$-modules." Annales de l’institut Fourier 37, no. 4 (1987): 161–66. http://dx.doi.org/10.5802/aif.1115.

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40

Ma, Linquan, and Wenliang Zhang. "Eulerian graded $\mathscr{D}$-modules." Mathematical Research Letters 21, no. 1 (2014): 149–67. http://dx.doi.org/10.4310/mrl.2014.v21.n1.a13.

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41

Richardson, Andrew S. "Attached Primes of Graded Modules." Communications in Algebra 31, no. 6 (January 7, 2003): 2603–13. http://dx.doi.org/10.1081/agb-120021884.

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42

Nâstâsescu, Constantin, Liu Shaoxue, and F. Van Oystaeyen. "Graded modules overG-sets II." Mathematische Zeitschrift 207, no. 1 (May 1991): 341–58. http://dx.doi.org/10.1007/bf02571393.

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43

Kanunnikov, A. L. "Orthogonal Graded Completion of Modules." Journal of Mathematical Sciences 221, no. 3 (January 21, 2017): 401–8. http://dx.doi.org/10.1007/s10958-017-3234-6.

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44

Al-Zoubi, Khaldoun, Rashid Abu-Dawwas, and Ibrahim Al-Ayyoub. "Graded semiprime submodules and graded semi-radical of graded submodules in graded modules." Ricerche di Matematica 66, no. 2 (December 19, 2016): 449–55. http://dx.doi.org/10.1007/s11587-016-0312-x.

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45

Guédénon, Thomas. "Semisimplicity of Locally Finite Graded R#H-Modules." Algebra Colloquium 16, no. 01 (March 2009): 109–22. http://dx.doi.org/10.1142/s1005386709000133.

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Let k be a field, Γ an abelian group with a bicharacter, R a colour algebra over k (i.e., a Γ-graded associative k-algebra with identity), H a Hopf colour k-algebra acting on R in such a way that R is a graded H-module algebra and the associated smash product R#H is a colour algebra. The aim of this paper is to study the semisimplicity of the category of H-locally finite Γ-graded R#H-modules. From our main result we deduce that if H is finite-dimensional and R is left graded-noetherian and graded-semisimple, then the colour algebra R#H is graded-semisimple if either H is graded-semisimple or if H is colour-cocommutative and R is colour-commutative and projective in the category of graded R#H-modules.

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46

Ghiasvand, Peyman, and Farkhonde Farzalipour. "Generalizations of graded second submodules." Acta Universitatis Sapientiae, Mathematica 13, no. 1 (August 1, 2021): 164–81. http://dx.doi.org/10.2478/ausm-2021-0009.

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Abstract Let G be a group with identity e. Let R be a graded ring, I a graded ideal of R and M be a G-graded R-module. Let ψ: Sgr(M) → S gr(M) ∪ {∅} be a function, where Sgr(M) denote the set of all graded submodules of M. In this article, we introduce and study the concepts of graded ψ -second submodules and graded I-second submodules of a graded R-module which are generalizations of graded second submodules of M and investigate some properties of this class of graded modules.

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47

Ooishi, Akira. "Reductions of graded rings and pseudo-flat graded modules." Hiroshima Mathematical Journal 18, no. 3 (1988): 463–77. http://dx.doi.org/10.32917/hmj/1206129612.

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48

Hu, Naihong. "The graded modules for the graded contact cartan algebras." Communications in Algebra 22, no. 11 (January 1994): 4475–97. http://dx.doi.org/10.1080/00927879408825082.

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49

FRANKILD, ANDERS, SRIKANTH IYENGAR, and PETER JØRGENSEN. "DUALIZING DIFFERENTIAL GRADED MODULES AND GORENSTEIN DIFFERENTIAL GRADED ALGEBRAS." Journal of the London Mathematical Society 68, no. 02 (September 25, 2003): 288–306. http://dx.doi.org/10.1112/s0024610703004496.

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50

Legrand, A. "Differential graded modules over a nonconnected differential graded algebra." Journal of Pure and Applied Algebra 72, no. 1 (July 1991): 53–66. http://dx.doi.org/10.1016/0022-4049(91)90129-p.

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