Article ID Journal Published Year Pages File Type
4598109 Journal of Pure and Applied Algebra 2007 7 Pages PDF
Abstract

A module MM is called product closed   if every hereditary pretorsion class in σ[M]σ[M] is closed under products in σ[M]σ[M]. Every module MM which is locally of finite length (every finitely generated submodule of MM has finite length) is product closed and every product closed module MM is semilocal (M/J(M)M/J(M) is semisimple). Let M∈R-Mod be product closed and projective in σ[M]σ[M]. It is shown that (1) MM is semiartinian; (2) if MM is finitely generated then MM satisfies the DCC on fully invariant submodules; (3) MM has finite length if MM is finitely generated and every hereditary pretorsion class in σ[M]σ[M] is MM-dominated. If the ring RR is commutative it is proven that MM is product closed if and only if MM is locally of finite length.

Keywords
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
, ,