PERFECT SYMMETRIC RINGS OF QUOTIENTS

Author:

VAŠ LIA1

Affiliation:

1. Department of Mathematics, Physics and Statistics, University of the Sciences in Philadelphia, 600 S. 43rd St. Philadelphia, PA 19104, USA

Abstract

Perfect Gabriel filters of right ideals and their corresponding right rings of quotients have the desirable feature that every module of quotients is determined solely by the right ring of quotients. On the other hand, symmetric rings of quotients have a symmetry that mimics the commutative case. In this paper, we study rings of quotients that combine these two desirable properties. We define the symmetric versions of a right perfect ring of quotients and a right perfect Gabriel filter — the perfect symmetric ring of quotients and the perfect symmetric Gabriel filter and study their properties. Then we prove that the standard construction of the total right ring of quotients [Formula: see text] can be adapted to the construction of the largest perfect symmetric ring of quotients — the total symmetric ring of quotients [Formula: see text]. We also demonstrate that Morita's construction of [Formula: see text] can be adapted to the construction of [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

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