On Properties Related To ∗–Reversible Rings
W. M. Fakieh *
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O.Box 80203, Jeddah 21589, Saudi Arabia.
N. A. Al-Juhani
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O.Box 80203, Jeddah 21589, Saudi Arabia and Department of Mathematics, University College of Umluj, Tabuk University, P.O.Box 741, Umluj 71491, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a class of -rings which is a generalization of*–reversible rings is introduced. A ring with involution * is called central *–reversible if for a,b ∈ R whenever ab= 0, b* a is central in R. Since every *–reversible ring is central *–reversible, sufficient conditions for central *–reversible rings to be*–reversible is studied. We show that some results of *–reversible rings can be extended to central *–reversible ring. For an Armendariz ring , we prove that is central *–reversible if and only if the polynomial ringR[X] is central *–reversible if and only if the Laurent polynomial ringR[x, x-1] is central *–reversible.
Keywords: ∗-reversible rings, weakly ∗–reversible rings, central reversible rings, central ∗–reversible rings