Strongly lifting modules and strongly dual Rickart modules

Abstract

The concepts of strongly lifting modules and strongly dual Rickart modules are introduced and their properties are studied and relations between them are given in this paper. It is shown that a strongly lifting module has the strongly summand sum property and the generalized Hopfian property, and a ring R is a strongly regular ring if and only if R_R is a strongly dual Rickart module, if and only if aRis a fully invariant direct summand of R_Rfor every a ∈ R.

Keywords

Lifting module / strongly lifting module / dual Rickart module / strongly dual Rickart module

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2016 Higher Education Press and Springer-Verlag Berlin Heidelberg