Associated Prime Submodules of Finitely Generated Modules

• Published in: Communications in algebra Vol. 33; no. 11; pp. 4259 - 4266
• Main Authors: Divaani-aazar, Kamran, Esmkhani, Mohammad Ali
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 01-10-2005
• Subjects: Associated prime ideals; Prime submodules; Quasi multiplication modules
• ISSN: 0092-7872; 1532-4125
• DOI: 10.1080/00927870500279027

Let R be a commutative ring with identity. For a finitely generated R-module M, the notion of associated prime submodules of M is defined. It is shown that this notion inherits most of the essential properties of the usual notion of associated prime ideals. In particular, it is proven that for a Noetherian multiplication module M, the set of associated prime submodules of M coincides with the set of M-radicals of primary submodules of M which appear in a minimal primary decomposition of the zero submodule of M. Also, Anderson's (
1994
) theorem is extended to minimal prime submodules in a certain type of modules.