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On Strongly 0-Prime Ideals in Near-Rings

Dheena, P., and Sivakumar, D., (2004) On Strongly 0-Prime Ideals in Near-Rings. Bulletin of the Malaysian Mathematical Sciences Society, 27 (1). pp. 77-85. ISSN 0126-6705

Full text not available from this repository.

Official URL: http://math.usm.my/bulletin/pdf/v27n1/v27n1p10.pdf

Affiliations

Annamalai University. Dept. of Mathematics
Annamalai University. Dept. of Mathematics

Abstract

In this paper we introduce the notion of strongly $\mathbf{0}$-prime ideals in near-rings similar to the notion introduced in rings. We give some characterizations of a near-ring $\mathbf{N}$ whose unique maximal nil ideal $\mathbf{N}_r(\mathbf{N})$ coincides with the set of all its
nilpotent elements $\mathbf{N}(\mathbf{N})$ by using its minimal strongly $\mathbf{0}$-prime ideals.

Item Type:Journal
Subjects:Q Science, Computer Science
ID Code:1379

1. N.J. Groenwald, Different prime ideals in near-rings, Comm. Algebra 19 (1991), 2667—2675.

2. C.Y. Hong and T.K. Kwak, On minimal strongly prime ideals, Comm. Algebra 28 (2000), 4867—4878.

3. N.K. Kim and T.K. Kwak, Minimal prime ideals in 2-primal rings, Math. Japonica 50 (1999), 415—420.

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

5. L.H. Rowan, Ring Theory I, Academic Press Inc., San Diego, 1988.

6. G.Y. Shin, Prime ideals and sheaf representation of a pseudo symmetric ring, Trans. Amer. Math. Soc. 184 (1973) 43—60.

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