SEMIPRIME SUBMODULES OF GRADED MULTIPLICATION MODULES

Title & Authors
SEMIPRIME SUBMODULES OF GRADED MULTIPLICATION MODULES
Lee, Sang-Cheol; Varmazyar, Rezvan;

Abstract
Let G be a group. Let R be a G-graded commutative ring with identity and M be a G-graded multiplication module over R. A proper graded submodule Q of M is semiprime if whenever $\small{I^nK{\subseteq}Q}$, where $\small{I{\subseteq}h(R)}$, n is a positive integer, and $\small{K{\subseteq}h(M)}$, then $\small{IK{\subseteq}Q}$. We characterize semiprime submodules of M. For example, we show that a proper graded submodule Q of M is semiprime if and only if grad\$(Q){\cap}h(M)
Keywords
Language
English
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