Affiliation:
1. Department of Mathematics, Jiaxing University, Jiaxing, Zhejiang 314001, China
Abstract
Let
be a class of some right
-modules that is closed under isomorphisms, and let
be a right
-module. Then
is called
-D3 if, whenever
and
are direct summands of
with
and
, then
is also a direct summand of
;
is called an
-D4 module, if whenever
where
and
are submodules of
and
, then every epimorphism
splits. Several characterizations and properties of these classes of modules are investigated. As applications, some new characterizations of semisimple Artinian rings, quasi-Frobenius rings, von Neumann regular rings, semiregular rings, perfect rings, semiperfect rings, hereditary rings, semihereditary rings, and PP rings are given.
Funder
Natural Science Foundation of Zhejiang Province
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