A NEW GENERALIZATION OF THE CENTER OF A NEAR-RING WITH APPLICATIONS TO POLYNOMIAL NEAR-RINGS

Abstract

Let N be a zero-symmetric right near-ring with identity. In 1993, S. Bagley introduced a construction for N[x], the near-ring of polynomials with coefficients from N. In this paper we study the central elements of N[x], C(N[x]), and we characterize C(N[x]) in terms of C(N) for a class of near-rings. We also introduce a new generalization for the center of a ring to the near-ring case, and we show that this new generalization yields a near-ring which properly contains C(N[x]) for a certain class of near-rings N.

Keywords:

• Polynomial near-ring
• Center

ACKNOWLEDGMENT

The author is grateful to Dr. K. C. Smith for his suggestions which helped to improve the presentation of an earlier version of this paper. This work is part of the author's doctoral dissertation at Texas A&M University under Dr. C.J. Maxson.