S-prime and S-weakly Prime Submodules

S-prime and S-weakly Prime Submodules

  • Emel Aslankarayiğit Uğurlu

Abstract

In this study, all rings are commutative with non-zero identity and all modules are considered to be unital. Let M be a left R-module. A proper submodule N of M is called an S-weakly prime
submodule if 0M ̸= f(m) ∈ N implies that either m ∈ N or f(M) ⊆ N, where f ∈ S = End(M) and m ∈ M. Some results concerning S-prime and S-weakly prime submodules are obtained. Then we study S-prime and S-weakly prime submodules of multiplication modules. Also for R-modules M1 and M2, we examine S-prime and S-weakly prime submodules of M = M1 ×M2, where S = S1 × S2, S1 = End(M1) and S2 = End(M2).

Published
2021-09-14
How to Cite
UĞURLU, Emel Aslankarayiğit. S-prime and S-weakly Prime Submodules. Eurasian Bulletin of Mathematics (ISSN: 2687-5632), [S.l.], v. 4, n. 2, p. 61-70, sep. 2021. ISSN 2687-5632. Available at: <http://www.ebmmath.com/index.php/EBM/article/view/80>. Date accessed: 27 nov. 2021.