On Properties Related To ∗–Reversible Rings

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.