On P_k and P_k' Near-Rings

Balakrishnan, R., and Suryanarayanan, S., (2000) On P_k and P_k' Near-Rings. Bulletin of the Malaysian Mathematical Sciences Society, 23 (1). pp. 9-24. ISSN 0126-6705

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Official URL: http://math.usm.my/bulletin/pdf/v23n1/v23n1p2.pdf

Affiliations

V.O.C College, Dept. of Mathematics
St. John's College, Dept. of Mathematics

Abstract

In page 297 of Pilz[4] a right near-ring $N$ is called a $C_{1}(C_{2})$ near-ring if $xN = xNx(Nx = xNx)$ for all $x$ in $N$ . Szasz, Frence, in [6] calls a ring $N$ , with the property $xN = xNx$ for all $x$ in $N$ , a $P_1$ -ring. We shall, in this paper, refer to a near-ring $N$ with the property $xN = xNx$ for all $x$ in $N$ , a $P_{1}(P_{1}')$ near-ring. Motivated by these concepts we introduce $P_k$ and $P_{k}'$ near-rings (Definition 2.1). We further generalize these concepts by introducing $P_{k}(r,m)$ and $P_{k}'(r,m)$ near-rings (Definition 3.1). We discuss the properties of all these newly introduced structures in detail. We also obtain complete charcterisations and structure theorems for such near rings.

Item Type:	Journal
Subjects:	Q Science, Computer Science
ID Code:	1382

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