Published January 1, 2010
| Version v1
Conference paper
Open
Weak Lifting Modules with Small Radical
Creators
- 1. Hacettepe Univ, Dept Math, TR-06800 Ankara, Turkey
- 2. Ain Shams Univ, Fac Educ, Dept Math, Cairo, Egypt
Description
Keskin and Tribak (2005) studied the structure of weak lifting modules with small radicals over commutative noetherian (local) rings. They proved that a module M is weak lifting if and only if M is a direct sum of local modules of some special type. Such modules were further studied by Tribak (2007). In this note we study weak lifting modules M with small radical over arbitrary rings. We prove that M is an irredundant sum M = Sigma(i is an element of I) M-i where each M-i is local and Sigma(i is an element of F) M-i is a summand of M for every finite subset F of I. Moreover Sigma(i is an element of F) M-i = circle plus(i is an element of F) K-i with K-i local. In particular a finitely generated weak lifting module is a direct sum of local modules. This generalizes the analogous result for finitely generated lifting modules.
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