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ESSENTIALLY SEMIMALL QUASI-DEDEKIND MODULES AND ANTI-HOPFIAN MODULES
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Let V be a ring with identity and S be a unitary left Module over V. An ????-Module S is essentially semismall quasi-Dedekind (ESSQD) whether Hom(S/H,S) = 0 H es S. A ring V is ESSQD if V is an ESSQD V-Module. An V -Module S is anti-hopfian if S is nonsimple and all nonzero factor Modules of S are isomorphic to S; that is for all , S Y S . In this paper we study the relationship between ESSQD with anti-hopfian Modules and continuous Modules. We also give some examples to illustrate these relationships.
Title: ESSENTIALLY SEMIMALL QUASI-DEDEKIND MODULES AND ANTI-HOPFIAN MODULES
Description:
Let V be a ring with identity and S be a unitary left Module over V.
An ????-Module S is essentially semismall quasi-Dedekind (ESSQD) whether Hom(S/H,S) = 0 H es S.
A ring V is ESSQD if V is an ESSQD V-Module.
An V -Module S is anti-hopfian if S is nonsimple and all nonzero factor Modules of S are isomorphic to S; that is for all , S Y S .
In this paper we study the relationship between ESSQD with anti-hopfian Modules and continuous Modules.
We also give some examples to illustrate these relationships.
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