FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

Ideals of distributive rings

A. A. Tuganbaev

Abstract

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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,b₂ ∈ A, $u$₁,u₂ ∈ T such that $au$₁=tb₁, $u$₂a=b₂t. 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.

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Last modified: June 17, 1998