t-PRIME SUBMODULES AND THEIR DECOMPOSITIONS

Document Type : Original Manuscript

Authors

1 Department of Mathematics, University of Hormozgan, Bandar Abbas, Hormozgan, Iran.

2 Department of Mathematics, Hacettepe University Beytepe Campus, Beytepe/ANKARA, Turkey.

10.22044/jas.2024.14373.1822

Abstract

Let $R$ be a commutative ring with identity. For $t\in N$, a proper submodule $N$ of an $R$-module $M$ is called a t-prime submodule if $rm\in N~(r\in R, m\in M)$, then $m\in N$ or $r^t\in (N:_RM)$. We obtain some other characterizations of t-prime submodules. Also by some other notions like t-secondary submodules, various properties of t-prime submodules are investigated. To this end, we deal with irreducible as well as reduced t-prime decompositions of a submodule. We provide several examples with illustrate our results.

Keywords

References

 1. M. F. Atiyah and I. G. McDonald, An introduction to commutative algebra, AddisionWesley, Reading, MA, 1969.
 
2. N. Khalid Abdullah, Irreducible submoduls and strongly irreducible submodules, Tikrit Journal of Pure Science, 17(4) (2012), 219–224.
 
3. S. Koç and U. Tekir, r-submodules and sr-Submodules, Turkish J. Math., 42(4) (2018), 1863–1876.
 
4. C. P. Lu, Prime submodules of modules, Comment. Math. Univ. Sancti. Pauli, 33(1) (1984), 61–69.
 
5. I. G. Macdonald, Secondary representation of modules over a commutative ring, Sympos. Math., XI (1973), 23–43.
 
6. R. L McCasland and M. E. Moore, Prime submodules, Comm. Algebra, 20(6) (1992), 1803–1817.
 
7. N. H. McCoy, The Theory of Rings, New York, Macmillan, 1964.
 
8. J. Moghaderi and A. Tercan, t-Prime submodules, U.P.B. Sci. Bull., Series A, 84(3) (2022), 31–40. 
Journal of Algebraic Systems
Volume 14, Issue 2
April 2026
Pages 369-381

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