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Dual of the duplication of a module along an ideal | ||
| Journal of Hyperstructures | ||
| دوره 15، شماره 1، شهریور 2026، صفحه 34-42 اصل مقاله (1.59 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2025.17652.1101 | ||
| نویسنده | ||
| Faranak Farshadifar* | ||
| Farhangian University | ||
| چکیده | ||
| Let R be a commutative ring with identity, I be an ideal of R, and M be an R-module. The amalgamated duplication of R along T, denoted by R \bowtie I, is the special subring of R × R defined by R \bowtie I := {(a, a + i) | a ∈ R, i ∈ I}. In this paper, we introduce and investigat a special kind of R \bowtie I-modules, called the dual of the duplication of M along I defined by M\bowtied I= {(m1, m2) ∈ M × M | m1 - m2 × (0 :M AnnR(I))}. In fact the R \bowtie I-module M\bowtied I is a dual of the R \bowtie I-module M \bowtie I := {(m,m') ∈ M × M | m - m' ∈ IM} which is introduced and studied by E. M. Bouba, N. Mahdou and M. Tamekkante. | ||
| کلیدواژهها | ||
| Amalgamated duplication؛ prime submodule؛ second submdule | ||
| مراجع | ||
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[1] H. Ansari-Toroghy and F. Farshadifar, The dual notion of multiplication modules. Taiwanese J. Math. 11 (4) (2007), 1189–1201. [2] A. Barnard, Multiplication modules. J. Algebra, 71 (1) (1981), 174-178. [3] E.M. Bouba, N. Mahdou and M. Tamekkante, Duplication of a module along an ideal. Acta Math. Hungar., 154 (1) (2018), 29–42. [4] J. Dauns, Prime modules, J. Reine Angew. Math., 298 (1978), 156–181. [5] F. Farshadifar, Survey on second submodules of modules over commutative rings, https://doi.org/10.48550/arXiv.2411.09333. [6] E.H. Feller and E.W. Swokowski, Prime modules. Canadian J. Math., 17 (1965), 1041–1052. [7] M. Issoual, N. Mahdou, N.A. Ozkirisci and E.Y. Celikel, On S-1-absorbing primary submodules. arXiv preprint arXiv:2203.04690, 2022. [8] N.V. Kasmatov, Bounds for the homological dimensions of pullbacks, J. Math. Sci. (N.Y.), 112 (2002), 4367-4370. [9] T. K. Lee and Y. Zhou, Reduced modules, In Rings, modules, algebras, and abelian groups, volume 236 of Lecture Notes in Pure and Appl. Math., pages 365-377. Dekker, New York, 2004. [10] E. A. Ugurlu, Generalizations of prime submodules over non-commutative rings, Journal of Hyperstructures, 11 (1) (2023), 65-83. [11] S. Yassemi, Coassociated primes of modules over commutative rings, Math. Scand., 10 (1997), 175–187. [12] S. Yassemi, The dual notion of prime submodules. Arch. Math. (Brno), 37 (4) (2001), 273–278. | ||
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آمار تعداد مشاهده مقاله: 145 تعداد دریافت فایل اصل مقاله: 78 |
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