具有同构定理对偶的环

Journal of Mathematical Sciences & Computational Mathematics Pub Date : 2020-11-02 DOI:10.15864/JMSCM.2104

I. Liaqat, Kaushef Salamat

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引用次数: 27

摘要

环R满足对偶的同构定理，如果R/Ra = 1(A)对于R中的所有元素A，其中1(A)表示左湮灭子。我们称这些环为左态环。例子包括所有单位正则环和某些左单列局部环。我们证明了每一个左态环都是右主内射，并以此来刻画左完全、右和左态环。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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RINGS WITH THE DUAL OF THE ISOMORPHISM THEOREM

A ring R satisfies the dual of the isomorphism theorem if R/Ra≅ 1(a) for all elements a of R, where 1(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.

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Journal of Mathematical Sciences & Computational Mathematics

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