Abstract
Let $R$ be a commutative ring with identity, $S$ a multiplicatively closed subset of $R$, and $M$ be an $R$-module.
In this paper, we study and investigate some properties of $S$-primary submodules of $M$. Among the other results, it is shown that this
class of modules contains the family of primary (resp. $S$-prime) submodules properly.
Keywords
Multiplicatively closed subset prime submodule $S$-prime submodule primary submodule $S$-primary submodule
References
- R. Ameri, On the prime submodules of multiplication modules, Int. J. Math. Math. Sci., 27 (2003), 1715-1724.
- D. D. Anderson and M. Winders, Idealization of a module, J. Commut. Algebra, 1(1) (2009), 3-56.
- J. Dauns, Prime modules, J. Reine Angew. Math., 298 (1978), 156-181.
- Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(4) (1988), 755-779.
- F. Farshadifar, S-secondary submodules of a module, Comm. Algebra, 49(4) (2021), 1394-1404.
- R. Gilmer, Multiplicative Ideal Theory, Queen's Papers in Pure and Applied Mathematics, 90, Queen's University, Kingston, 1992.
- C. P. Lu, A module whose prime spectrum has the surjective natural map, Houston J. Math., 33(1) (2007), 125-143.
- R. L. McCasland and M. E. Moore, On radicals of submodules of finitely generated modules, Canad. Math. Bull., 29(1) (1986), 37-39.
- R. L. McCasland and M. E. Moore, Prime submodules, Comm. Algebra, 20(6) (1992), 1803-1817.
- M. Nagata, Local Rings, Interscience Tracts in Pure and Applied Mathematics, 13, 1962.
- E. Sevim, T. Arabaci, U. Tekir and S. Koc, On S-prime submodules, Turkish J. Math., 43(2) (2019), 1036-1046.
- F. Wang and H. Kim, Foundations of Commutative Rings and Their Modules, Algebra and Applications, 22, Springer, Singapore, 2016.
Abstract
References
- R. Ameri, On the prime submodules of multiplication modules, Int. J. Math. Math. Sci., 27 (2003), 1715-1724.
- D. D. Anderson and M. Winders, Idealization of a module, J. Commut. Algebra, 1(1) (2009), 3-56.
- J. Dauns, Prime modules, J. Reine Angew. Math., 298 (1978), 156-181.
- Z. A. El-Bast and P. F. Smith, Multiplication modules, Comm. Algebra, 16(4) (1988), 755-779.
- F. Farshadifar, S-secondary submodules of a module, Comm. Algebra, 49(4) (2021), 1394-1404.
- R. Gilmer, Multiplicative Ideal Theory, Queen's Papers in Pure and Applied Mathematics, 90, Queen's University, Kingston, 1992.
- C. P. Lu, A module whose prime spectrum has the surjective natural map, Houston J. Math., 33(1) (2007), 125-143.
- R. L. McCasland and M. E. Moore, On radicals of submodules of finitely generated modules, Canad. Math. Bull., 29(1) (1986), 37-39.
- R. L. McCasland and M. E. Moore, Prime submodules, Comm. Algebra, 20(6) (1992), 1803-1817.
- M. Nagata, Local Rings, Interscience Tracts in Pure and Applied Mathematics, 13, 1962.
- E. Sevim, T. Arabaci, U. Tekir and S. Koc, On S-prime submodules, Turkish J. Math., 43(2) (2019), 1036-1046.
- F. Wang and H. Kim, Foundations of Commutative Rings and Their Modules, Algebra and Applications, 22, Springer, Singapore, 2016.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | January 17, 2022 |
| Published in Issue | Year 2022 Volume: 31 Issue: 31 |