Open AccessIsomorphism between Endomorphism Rings of Modules over A Semisimple Ring
Author(s) -
Hery Susanto,
Santi Irawati,
Indriati Nurul Hidayah,
Irawati
Publication year - 2020
Publication title -
journal of the indonesian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2460-0245
pISSN - 2086-8952
DOI - 10.22342/jims.26.2.824.170-174
Subject(s) - mathematics , simple module , endomorphism ring , primitive ring , isomorphism (crystallography) , endomorphism , ring (chemistry) , division ring , pure mathematics , simple ring , semisimple module , noncommutative ring , simple (philosophy) , principal ideal ring , von neumann regular ring , module , artinian ring , discrete mathematics , algebra over a field , projective module , finitely generated abelian group , division (mathematics) , arithmetic , commutative ring , crystallography , crystal structure , noetherian , philosophy , chemistry , epistemology , commutative property , organic chemistry
Our question is what ring R which all modules over R are determined, up to isomorphism, by their endomorphism rings? Examples of this ring are division ring and simple Artinian ring. Any semi simple ring does not satisfy this property. We construct a semi simple ring R but R is not a simple Artinian ring which all modules over R are determined, up to isomorphism, by their endomorphism rings.