Anticommutativity of symmetric elements under generalized oriented involutions

Abstract

Let R be a ring with whose unit group is denoted by G a group with involution and a nontrivial group homomorphism, with satisfying for all Let RG be the group ring of G over R and define the involution in RG by In this article, we will classify the group rings RG such that is anticommutative, where is the largest subset of that can satisfy anticommutativity under Besides that, previous results about or will be extended.Communicated by S. Sehgal