• A NOTE ON B1-NEAR-FIELD SPACES OVER REGULAR -NEAR-RINGS (B1 - NFS-R--NR)

Abstract

The aim of Dr N V Nagendram in this paper is to extend the concepts of B₁ near-rings and after in depth study to introduce the concepts of B₁ – near-field spaces and strong B₁ – near-field spaces.  We say that a right near-field space N is a B₁ – near-field space if for every a Î N, there exists x Î N^* where N^* = N – {0}, such that N ax = N xa. By way of generalization, we define N as a strong B₁ – near-field space if N ab = N ba " a, b Î N. Dr. N. V. Nagendram discuss some of their properties and obtain a characterization and also a structure theorem.