| Yazarlar |
Prof. Dr. Akın Osman ATAGÜN
Kırşehir Ahi Evran Üniversitesi, Türkiye |
| Özet |
| 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 Kelimeler |
| Near-ring, Prime ideal, IFP, Nilpotent element, Equiprime near-ring |
| Makale Türü | Özgün Makale |
| Makale Alt Türü | SSCI, AHCI, SCI, SCI-Exp dergilerinde yayımlanan tam makale |
| Dergi Adı | HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS |
| Dergi ISSN | 2651-477X |
| Dergi Tarandığı Indeksler | SCI-Expanded |
| Dergi Grubu | Q3 |
| Makale Dili | İngilizce |
| Basım Tarihi | 01-2010 |
| Cilt No | 39 |
| Sayı | 1 |
| Sayfalar | 17 / 21 |
