On some Montgomery's results on algebras with involution in superalgebras

Abstract

We study semiprime superalgebras with superinvolution whose symmetric or skewsymmetric elements are assumed to be regular or nilpotent, and superalgebras in which xx* = 0 implies x*x = 0.

Nilpotent superderivations in prime superalgebras

“…Superinvolutions in associative superalgebras have been a topic of great interest. We highlight the works of J. Laliena [21] on the description of the derived superalgebra [K, K] of a semiprime superalgebra with superinvolution, the papers [22] and [23] of J. Laliena and R. Rizzo on the extension of results of C. Lanski and S. Montgomery to associative superalgebras with superinvolution, and the recent works of T. S. do Nascimento, A. C. Vieira, A. Giambruno, A. Ioppolo, D. La Mattina, F. Martino ( [5], [10], [11], [12], [18]) on superinvolutions in superalgebras related to polynomial identities and related to the growth of certain substructures of the superalgebras.…”