In this paper, we consider p-Banach algebras endowed with a generalized involution. We show that various C∗-like conditions force the algebra to be C∗-algebra under an equivalent norm
A *-ring $R$ is called strongly nil *-clean if every element of $R$ is the sum of a projection and a nilpotent element that commute with each other. In this paper we investigate some properties of strongly nil *-rings and prove that $R$... more
A *-ring $R$ is called strongly nil *-clean if every element of $R$ is the sum of a projection and a nilpotent element that commute with each other. In this paper we investigate some properties of strongly nil *-rings and prove that $R$ is a strongly nil *-clean ring if and only if every idempotent in $R$ is a projection, $R$ is periodic, and $R/J(R)$ is Boolean. We also prove that a *-ring $R$ is commutative, strongly nil *-clean and every primary ideal is maximal if and only if every element of R is a projection.
Let R be a -prime ring with characteristic not 2; Z(R) be the center of R; I be a nonzero -ideal of R; ; : R ! R be two automorphisms, d be a nonzero ( ; )-derivation of R and h be a nonzero derivation of R: In the present paper, it... more
Let R be a -prime ring with characteristic not 2; Z(R) be the center of R; I be a nonzero -ideal of R; ; : R ! R be two automorphisms, d be a nonzero ( ; )-derivation of R and h be a nonzero derivation of R: In the present paper, it is shown that (i) If d (I) C ; and commutes with then R is commutative. (ii) Let and commute with : If a 2 I \ S (R) and [d(I); a] ; C ; then a 2 Z(R): (iii) Let ; and h commute with : If dh (I) C ; and h (I) I then R is commutative.
Let FG be the group algebra of a finite group G over a field F of characteristic p . We give the maximal number of the non-isomorphic unitary subgroups with respect to the involutions of FG which arise from G . Furthermore, we... more
Let FG be the group algebra of a finite group G over a field F of characteristic p . We give the maximal number of the non-isomorphic unitary subgroups with respect to the involutions of FG which arise from G . Furthermore, we characterize the group algebras with Hamiltonian unitary subgroup under the canonical involution, where G is a finite p -group and F is a finite field of characteristic p . Let FG denote the group algebra of a non-abelian group of order 8 over a finite field of characteristic two. We also describe the structure of the non-isomorphic unitary subgroups of FG linked to all the involutions which arise from G .
