“School of Mathematics”
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| Paper IPM / M / 7399 |
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| Abstract: | |||||
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An endoprime R-module M is a nonzero module whose nonzero
fully invariant submodules are faithful over END(MR). Such
modules have prime endomorphism rings. The class of endoprime
modules properly contains the class of prime modules in the sense
of Zelmanowitz [5], and the class of prime modules with condition
(∗) of Wisbauer [4]. While over commutative rings, endoprime
modules are prime, in general, prime and endoprime are different
conditions. A nonzero right R-Module M is a direct sum of
isomorphic simple modules if and only if each nonzero element of
σ[M] is an endoprime module. Various properties of
endoprime modules including their Morita invariance, are obtained,
and the structure of endomprphism rings of certain endoprime
modules are determined.
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