Abstract
A near-ring N is called an IFP near-ring provided that for all a, b, n ∈
N, ab = 0 implies anb = 0. In this study, the IFP condition in a nearring 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 nearring 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 nearrings.
References
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Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | July 3, 2019 |
| Published in Issue | Year 2010 Volume: 39 Issue: 1 |