P-STRONGLY REGULAR NEAR-RINGS

Title & Authors
P-STRONGLY REGULAR NEAR-RINGS
Dheena, P.; Jenila, C.;

Abstract
In this paper we introduce the notion of P-strongly regular near-ring. We have shown that a zero-symmetric near-ring N is P-strongly regular if and only if N is P-regular and P is a completely semiprime ideal. We have also shown that in a P-strongly regular near-ring N, the following holds: (i) $\small{Na}$ + P is an ideal of N for any $\small{a{\in}N}$. (ii) Every P-prime ideal of N containing P is maximal. (iii) Every ideal I of N fulfills I + P = $\small{I^2}$ + P.
Keywords
P-regular;P-strongly regular;P-prime ideal;completely semiprime ideal;
Language
English
Cited by
References
1.
V. A. Andrunakievich, Regularity of a ring with respect to right ideals, Dokl. Akad. Nauk SSSR. 310 (1990), no. 2, 267-272.

2.
A. O. Atagun, IFP Ideals in near-rings, Hacet. J. Math. Stat. 39 (2010), no. 1, 17-21.

3.
S. J. Choi, Quasiideals of a P-Regular Near-Ring, Int. J. Algebra 4 (2010), no. 9-12, 501-506.

4.
P. Dheena, On strongly regular near-rings, J. Indian Math. Soc. (N.S.) 49 (1985), no. 3-4, 201-208.

5.
G. Mason, Strongly regular near-rings, Proc. Edinburgh Math. Soc. (2) 23 (1980), no. 1, 27-35.

6.
G. Pilz, Near-Rings, North-Holland, Amsterdam, 1983.

7.
I. Yakabe, Regular near-rings without nonzero nilpotent elements, Proc. Japan Acad. Ser. A Math. Sci. 65 (1989), no. 6, 176-179.