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