Ring Endomorphisms Satisfying Z-symmetric Property

Abstract

The notion of α-skew Z-symmetric rings is introduced as a generalization of Z-symmetric rings. We prove that the notions of α-skew Z-symmetric rings and Z-symmetric rings are independent, and we give some sufficient conditions over which these notions are equivalent. We investigate some basic properties of α-skew 
Z-symmetric rings and give a characterization of them. Moreover, we provide some characterizations of α-skew Z-symmetric rings utilizing the Dorroh extension, triangular matrix ring etc. Finally, we generalize some results of Z-symmetric rings to α-skew Z-symmetric rings.

Key words and phrases. endomorphisms; Z-symmetric rings, α-skew reversible rings, α-skew Z-symmetric rings.

2010 Mathematics Subject Classification. 16W20, 16U99, 16D80