2019•Journal of Physics Conference SeriesOpen access

Isomorphism between endomorphism rings of modules over a semi simple ring

Hery Susanto, S Irawati, Indriati Nurul Hidayah, Irawati

Abstract

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.

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Key concepts: Mathematics, Primitive ring, Simple ring, Division ring, Endomorphism, Ring (chemistry), Simple module, Isomorphism (crystallography)