LEFT QUASI-MORPHIC RINGS

Camillo V; Nicholson WK; Wang Z

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LEFT QUASI-MORPHIC RINGS

机译：左拟态环

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摘要

A ring R is called left quasi-morphic if, for each a epsilon R, there exist b and c in R such that Ra = 1(b) and 1(a) = Rc (where 1(x) is the left annihilator). Every (von Neumann) regular ring is left quasi-morphic, as is every left morphic ring (b = c above). The main theorem of this paper is that, in a left quasi-morphic ring, finite intersections and finite sums of principal left ideals are again principal. This leads to structure theorems when mild finiteness conditions are imposed. In an earlier paper, the first two authors showed that left and right quasi-morphic rings have both these properties (on both sides), and used this to give a new characterization of the artinian principal ideal rings: They are just the left and right quasi-morphic rings with ACC on principal annihilators r(a), a epsilon R. Some extensions of this result are presented here.

机译：如果对于每个εR，R中都存在b和c，使得Ra = 1（b）和1（a）= Rc（其中1（x）是左an灭子），则将R称为左准晶。每个（冯·诺依曼）正则环都是左准准环，每个左态环都是（上面b = c）。本文的主要定理是，在左拟晶环中，主左理想的有限交点和有限和再次成为主。当施加适度的有限性条件时，这导致结构定理。在较早的论文中，前两位作者表明左和右准晶环同时具有这两个属性（在两侧上），并以此为对阿蒂尼亚原理的理想环的新描述：它们分别是左和右在主an灭子r（a），εR上具有ACC的准晶环。此处给出了该结果的一些扩展。

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《Journal of algebra and its applications》 |2008年第6期|共9页
作者
Camillo V; Nicholson WK; Wang Z;
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正文语种 eng
中图分类代数、数论、组合理论;
关键词
Quasi-morphic ring; regular ring; principal left ideal ring; left Bezout ring;

机译：准环;正则环;主左理想环;左Bezout环;

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1. Semiprime left quasi-morphic rings [J] . Nicholson W.K. Journal of algebra and its applications . 2013,第7期

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3. Regular elements in quasi-morphic rings [J] . Chen H. Communications in algebra . 2011,第4期

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LEFT QUASI-MORPHIC RINGS

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