No abstract

Let [Formula: see text] be a ring and [Formula: see text] an idempotent of [Formula: see text], [Formula: see text] is called an [Formula: see text]-symmetric ring if [Formula: see text] implies [Formula: see text] for all [Formula: see text]. Obviously, [Formula: see text] is a symmetric ring if and only if [Formula: see text] is a [Formula: see text]-symmetric ring. In this paper, we show that a ring [Formula: see text] is [Formula: see text]-symmetric if and only if [Formula: see text] is left semicentral and [Formula: see text] is symmetric. As an application, we show that a ring [Formula: see text] is left min-abel if and only if [Formula: see text] is [Formula: see text]-symmetric for each left minimal idempotent [Formula: see text] of [Formula: see text]. We also introduce the definition of strongly [Formula: see text]-symmetric ring and prove that [Formula: see text] is a strongly [Formula: see text]-symmetric ring if and only if [Formula: see text] and [Formula: see text] is a symmetric ring. Finally, we introduce [Formula: see text]-reduced ring and study some properties of it.

No abstract

No abstract

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz