Abstract
In this paper we introduce the notion of equiprime N-ideals where N is a near-ring. We consider the interconnections of equiprime, 3-prime and completely prime N-ideals of a monogenic N-group Γ. We show that if P is an equiprime N-ideal of Γ, then (P : Γ)N is an equiprime ideal of N, and that the converse holds when N is a right permutable near-ring and Γ is a monogenic N-group.
Keywords
Prime near-ring Prime ideal Prime N-group Equiprime N-ideal 2000 AMS Classification: 16 Y 30
References
- Atag¨un, A. O. IFP ideals in near-rings, Hacet. J. Math. Stat. 39 (1), 17–21, 2010.
- Atag¨un, A. O. and Groenewald, N. J. Primeness in near-rings with multiplicative semi-group satisfying ‘The Three Identities’, J. Math. Sci. Adv. Appl. 2 (1), 137–145, 2009.
- Birkenmeier, G. and Heatherly, H. Medial near-rings, Monatsh. Math. 107, 89–110, 1989.
- Birkenmeier, G. and Heatherly, H. Left self distributive near-rings, J. Austral. Math. Soc. (Series A) 49, 273–296, 1990.
- Booth, G. L., Groenewald, N. J. and Veldsman, S. A Kurosh-Amitsur prime radical for near-rings, Comm. Algebra 18 (9), 3111–3122, 1990.
- Booth, G. L. and Groenewald, N. J. Equiprime left ideals and equiprime N-groups of a near-ring, Contributions to General Algebra 8, 25–38, 1992.
- C¸ allıalp, F. and Tekir, ¨U. On the prime radical of a module over a noncommutative ring, Taiwan. J. Math. 8 (2), 337–341, 2004.
- Groenewald, N. J. Different prime ideals in near-rings, Comm. Algebra 19 (10), 2667–2675,
- Holcombe, W. L. M. Primitive near-rings (Doctoral Dissertation, University of Leeds, 1970).
- Juglal, S., Groenewald, N. J. and Lee, E. K. S. Different prime R-ideals, Algebr. Colloq. 17, –904, 2010.
- Lomp, C. and Pe˜na, A. J. A note on prime modules, Divulgaciones Matem´aticas 8 (1), 31–42, Pilz, G. Near-rings (North-Holland, Amsterdam, 1983).
- Ramakotaiah, D. and Rao, G. K. IFP near-rings, J. Austral. Math. Soc. (Series A) 27, –370, 1979.
- Veldsman, S. On equiprime near-rings, Comm. Algebra 20 (9), 2569–2587, 1992.
- Wisbauer, R. On prime modules and rings, Comm. Algebra 11 (20), 2249–2265, 1983.
Abstract
References
- Atag¨un, A. O. IFP ideals in near-rings, Hacet. J. Math. Stat. 39 (1), 17–21, 2010.
- Atag¨un, A. O. and Groenewald, N. J. Primeness in near-rings with multiplicative semi-group satisfying ‘The Three Identities’, J. Math. Sci. Adv. Appl. 2 (1), 137–145, 2009.
- Birkenmeier, G. and Heatherly, H. Medial near-rings, Monatsh. Math. 107, 89–110, 1989.
- Birkenmeier, G. and Heatherly, H. Left self distributive near-rings, J. Austral. Math. Soc. (Series A) 49, 273–296, 1990.
- Booth, G. L., Groenewald, N. J. and Veldsman, S. A Kurosh-Amitsur prime radical for near-rings, Comm. Algebra 18 (9), 3111–3122, 1990.
- Booth, G. L. and Groenewald, N. J. Equiprime left ideals and equiprime N-groups of a near-ring, Contributions to General Algebra 8, 25–38, 1992.
- C¸ allıalp, F. and Tekir, ¨U. On the prime radical of a module over a noncommutative ring, Taiwan. J. Math. 8 (2), 337–341, 2004.
- Groenewald, N. J. Different prime ideals in near-rings, Comm. Algebra 19 (10), 2667–2675,
- Holcombe, W. L. M. Primitive near-rings (Doctoral Dissertation, University of Leeds, 1970).
- Juglal, S., Groenewald, N. J. and Lee, E. K. S. Different prime R-ideals, Algebr. Colloq. 17, –904, 2010.
- Lomp, C. and Pe˜na, A. J. A note on prime modules, Divulgaciones Matem´aticas 8 (1), 31–42, Pilz, G. Near-rings (North-Holland, Amsterdam, 1983).
- Ramakotaiah, D. and Rao, G. K. IFP near-rings, J. Austral. Math. Soc. (Series A) 27, –370, 1979.
- Veldsman, S. On equiprime near-rings, Comm. Algebra 20 (9), 2569–2587, 1992.
- Wisbauer, R. On prime modules and rings, Comm. Algebra 11 (20), 2249–2265, 1983.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Research Article |
| Authors | |
| Publication Date | March 1, 2011 |
| Published in Issue | Year 2011 Volume: 40 Issue: 3 |