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 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

 Fundam. Prikl. Mat., 1998, Volume 4, Issue 2, Pages 791–794 (Mi fpm328)

Short communications

Ideals of distributive rings

A. A. Tuganbaev

Moscow Power Engineering Institute (Technical University)

Abstract: 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.

Full text: PDF file (208 kB)

Bibliographic databases:
UDC: 512.55

Citation: A. A. Tuganbaev, “Ideals of distributive rings”, Fundam. Prikl. Mat., 4:2 (1998), 791–794

Citation in format AMSBIB
\Bibitem{Tug98} \by A.~A.~Tuganbaev \paper Ideals of distributive rings \jour Fundam. Prikl. Mat. \yr 1998 \vol 4 \issue 2 \pages 791--794 \mathnet{http://mi.mathnet.ru/fpm328} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1801194} \zmath{https://zbmath.org/?q=an:0963.16001}