Rings with the dual of the isomorphism theorem

A ring R satisfies the dual of the isomorphism theorem if R/ Ra≅ l( a) for all elements a of R, where l( a) denotes the left annihilator. We call these rings left morphic. Examples include all unit regular rings and certain left uniserial local rings. We show that every left morphic ring is right pr...

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Bibliographic Details
Published inJournal of algebra Vol. 271; no. 1; pp. 391 - 406
Main Authors Nicholson, W.K., Sánchez Campos, E.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 2004
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Summary:A ring R satisfies the dual of the isomorphism theorem if R/ Ra≅ l( a) for all elements a of R, where l( a) denotes the left annihilator. We call these rings left morphic. Examples include all unit regular rings and certain left uniserial local rings. We show that every left morphic ring is right principally injective, and use this to characterize the left perfect, right and left morphic rings.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2002.10.001