RING ENDOMORPHISMS SATISFYING Z-SYMMETRIC PROPERTY

The notion of alpha-skew Z-symmetric rings is introduced as a generalization of Z-symmetric rings. We prove that the notions of alpha-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 alpha-skew Z-symmetric rings and give a characterization of them. Moreover, we provide some characterizations of alpha-skew Z-symmetric rings utilizing the Dorroh extension, triangular matrix ring etc. Finally, we generalize some results of Z-symmetric rings to alpha-skew Z-symmetric rings.