Some commutativity criteria for prime rings with involution involving symmetric and skew symmetric elements

N. A.  Dar; S.  Ali; A.  Abbasi; M.  Ayedh

doi:10.37863/umzh.v75i4.6751

N. A. Dar Govt. HSS, Kaprin, Shopian Jammu and Kashmir, India
S. Ali Aligarh Muslim University, India https://orcid.org/0000-0001-5162-7522
A. Abbasi Madanpalle Institute Technology and Science, India
M. Ayedh Aligarh Muslim University, India

DOI: https://doi.org/10.37863/umzh.v75i4.6751

Keywords: Generalized derivation, involution, prime ring, symmetric and skew symmetric element

Abstract

UDC 512.5

We study the Posner second theorem [Proc. Amer. Math. Soc., 8, 1093–1100 (1957)] and strong com\-mu\-ta\-tivity preserving problem for symmetric and skew symmetric elements involving generalized derivations on prime rings with involution. The obtained results cover numerous known theorems. We also provide examples showing that the obtained results hold neither in the case of involution of the first kind, nor in the case where the ring is not prime.

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