Some Remarks on Primal Submodules - Atani, S. Ebrahimi; Darani, A. Yousefian (Sarajevo Journal of Mathematics, 2024)
In this paper, we study the primal submodules of a module over a commutative ring with non-zero identity. We generalize the primal decomposition of ideals (see [2]) to that of submodules. Let $R$ be a commutative ring, $M$ an $R$-module and $N$ a submodule of $M$. We establish a decomposition of $N$ as an intersection of primal submodules of $M$. We show that if $R$ is a Prüfer domain of finite character, then $N$ has a primal decomposition. Also we prove that the representation of submodules as reduced intersections of primal submodules is unique. 2000 Mathematics Subject Classification. 13A05, 13F05, 20M14