(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 2, PAGES 791-794

## Ideals of distributive rings

A. A. Tuganbaev

Abstract

View as HTML     View as gif image    View as LaTeX source

 Let $P$ be a prime ideal of a distributive ring $A$, and let $T$ be the set of all elements $t\in A$ such that $t+P$ is a regular element of the ring $A/P$. Then for any elements $a\in A$, $t\in T$ there exist elements $b_1,b_2\in A$, $u_1,u_2\in T$ such that $au_1=tb_1$, $u_2a=b_2t$. If either all square-zero elements of $A$ are central or $A$ satisfies the maximum conditions for right and left annihilators, then the classical two-sided localization $A_P$ exists and is a distributive ring. 

All articles are published in Russian.

 Main page Editorial board Instructions to authors Contents of the journal

Location: http://mech.math.msu.su/~fpm/eng/98/982/98227t.htm