IFP ideals in near-rings

ATAGÜN, AKIN OSMAN

IFP ideals in near-rings

Akın Osman ATAGÜN (Bozok Üniversitesi, Yozgat, Türkiye)

Hacettepe Journal of Mathematics and Statistics

1 0

Yıl: 2010 Cilt: 39 Sayı: 1 Sayfa Aralığı: 17 - 21 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

IFP ideals in near-rings

Öz:

A near-ring N is called an IFP near-ring provided that for all a, b, n $in$ N, ab = 0 implies anb = 0. In this study, the IFP condition in a near- ring is extended to the ideals in near-rings. If N/P is an IFP near-ring, where P is an ideal of a near-ring N, then we call P as the IFP-ideal of N. The relations between prime ideals and IFP-ideals are investigated. It is proved that a right permutable or left permutable equiprime near- ring has no non-zero nilpotent elements and then it is established that if N is a right permutable or left permutable finite near-ring, then N is a near-field if and only if N is an equiprime near-ring. Also, attention is drawn to the fact that the concept of IFP-ideal occurs naturally in some near-rings, such as p-near-rings, Boolean near-rings, weakly (right and left) permutable near-rings, left (right) self distributive near-rings, left (right) strongly regular near-rings and left (w-) weakly regular near- rings.

Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Argac, N. and Groenewald, N. J. Weakly and strongly regular near-rings, Alg. Coll. 12,121-130, 2005.
[2] Bell, H. E. Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc.2, 363-368, 1970.
[3] Bell, H. E. Certain near-rings are rings, J. London Math. Soc. II 4, 264-270, 1971.
[4] Birkenmeier, G. and Heatherly, H. Medial near-rings, Mh. Math. 107, 89-110, 1989.
[5] Birkenmeier, G. and Heatherly, H. Left self distributive near-rings, J. Austral. Math.Soc.(Series A) 49, 273-296, 1990.
[6] Birkenmeier, G., Heatherly, H. and Lee, E. Prime ideals in near-rings, Results Math. 24,27-48, 1993.
[7] Birkenmeier, G. and Groenewald, N. J. Near-rings in which each prime factor is simple, Math. Pannon. 10, 257-269, 1999.
[8} Booth, G., Groenewald, N. J. and Veldsman, S. A Kurosh-Amitsur prime radical for near Comm. Algebra 18, 3111-3122, 1990.
[9] Dheeila, P. and Rejeswari, C. Weakly regular near-rings, Indian J. Pure and Appl. Math.28, 1207-1213, 1997.
[10] Groenewald, N. J. Different prime ideals in near-rings, Comm. Algebra 10, 2667-2675, 1991.
[11] Groenewald, N. J. The completely prime radical in near-rings, Acta Math. Hungar. 51,301-305, 1988.
[12] Ligh, S. On the commutativity of near-rings III, Bull. Austral. Math. Soc. 6, 459-464, 1972.
[13] Mason, G. Strongly regular near-rings, Proc. Edinburgh Math. Soc. 23, 27-35, 1980.
[14] Pilz, G. Near-rings (North-Holland, 1983).
[15] Plasser, K. Subdirekte darstellung von ringen und fastringen mit boolschen eigenzchaften(Diplomarbeit, Univ. Linz, Austria, 1974).
[16] Veldsman, S. On equiprime near-rings, Comm. Algebra 20, 2569-2587, 1992.

APA	ATAGÜN A (2010). IFP ideals in near-rings. , 17 - 21.
Chicago	ATAGÜN AKIN OSMAN IFP ideals in near-rings. (2010): 17 - 21.
MLA	ATAGÜN AKIN OSMAN IFP ideals in near-rings. , 2010, ss.17 - 21.
AMA	ATAGÜN A IFP ideals in near-rings. . 2010; 17 - 21.
Vancouver	ATAGÜN A IFP ideals in near-rings. . 2010; 17 - 21.
IEEE	ATAGÜN A "IFP ideals in near-rings." , ss.17 - 21, 2010.
ISNAD	ATAGÜN, AKIN OSMAN. "IFP ideals in near-rings". (2010), 17-21.

APA	ATAGÜN A (2010). IFP ideals in near-rings. Hacettepe Journal of Mathematics and Statistics, 39(1), 17 - 21.
Chicago	ATAGÜN AKIN OSMAN IFP ideals in near-rings. Hacettepe Journal of Mathematics and Statistics 39, no.1 (2010): 17 - 21.
MLA	ATAGÜN AKIN OSMAN IFP ideals in near-rings. Hacettepe Journal of Mathematics and Statistics, vol.39, no.1, 2010, ss.17 - 21.
AMA	ATAGÜN A IFP ideals in near-rings. Hacettepe Journal of Mathematics and Statistics. 2010; 39(1): 17 - 21.
Vancouver	ATAGÜN A IFP ideals in near-rings. Hacettepe Journal of Mathematics and Statistics. 2010; 39(1): 17 - 21.
IEEE	ATAGÜN A "IFP ideals in near-rings." Hacettepe Journal of Mathematics and Statistics, 39, ss.17 - 21, 2010.
ISNAD	ATAGÜN, AKIN OSMAN. "IFP ideals in near-rings". Hacettepe Journal of Mathematics and Statistics 39/1 (2010), 17-21.