BAER SPECIAL RINGS AND REVERSIBILITY

Abstract

Abstract. In this paper, we apply some properties of reversiblerings, Baerness of xed rings, skew group rings and Morita Contextrings to get conditions that shows xed rings, skew group ringsand Morita Context rings are reversible. Moreover, we investigateconditions in which Baer rings are reversible and reversible ringsare Baer. 1. IntroductionThroughout this paper all rings are associative rings with identity un-less otherwise stated. Let Rbe a ring. We denote S r (R)(resp. S l (R) bythe set of right(resp. left)semi-central idempotents in R. For a nonemptysubset Xof R, r R (X)(resp. l R (X)) will be denoted by the right(resp.left)annihilator of X in R. In 1990, Habeb studied commutativering in [5]. A ring R is called commutative, if ab = 0 impliesba= 0 for any a;b2R. In 1999[4] used the terminology reversiblering instead of zero commutative . Obviously, a commutative ringis reversible ring, but converse is not true. In fact every reversible ringis semi-commutative but converse is not true(for more details see [12]).Moreover, A ring Ris called right (resp. left)symmetric ring, if rst= 0implies rts= 0 (resp. srt= 0), for any r;s;t2R. It is easy to checkthat reduced ring is symmetric ring,a symmetric ring with identity isa reversible and a reversible ring is semi-commutative. In 2002, Marks[16] studied conditions in which a group ring becomes reversible, andstudied some relationships of among symmetric rings, reduced rings andreversible rings. Baer ring is one of the classic rings and it is appliedwidely in the eld of C*-algebra, Von Neumann algebra and Coding