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

Dr. N. V. NAGENDRAM*

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.


Keywords


B1–near-ring, strong B1–near-ring, near-field, near-field space, sub near-field space, B1–near-field spaces, B1 – sub near-field spaces.

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