… As an easy consequence of Lemma 1.1 we have the following elementwise characterizations
of v-prime ideals : … (i) If N E Jo, then P a N is a 0-prime ideal if and only if for a,b E N …

… An ideal I of a near-ring R is a type one prime ideal if whenever aRb ~ I, then a … prime ideals
and type one prime ideals in near-rings. It also develops properties of type one prime ideals, …

… of prime ideals and prime radicals in near-rings [1], [2], [4], [5]. The basic results for prime ideals
(also called type 0 prime ideals … prime ideals, respectively completely prime ideals, of the …

… of 2—prime 0-symmetric near-rings is hereditary and essentially closed, and we show that
the 2-prime radical is not Kurosh-Amitsur for arbitrary near-rings. The 1-prime radical is not …

… s-prime ideals in general rings and in [6] he obtained corresponding results for near-rings. …
PRELIMINARY DEFINITIONS We will denote a near-ring by N and the class of all near-rings …

… some results to get some relations between a semi-prime ideal 7 and the minimal prime
ideals of 7 in N. We have the following for s-semi-prime ideals and quasi-minimal s-prime ideals. …

… near-rings is a special class in the sense of Kaarli [6]. We also show that if N is any distributively
generated nearring… M, coincides with the intersection of all the strongly prime ideals of N. …

… We end this section with a structure theorem for finite prime dg nearrings which gives a
relationship between all the cyclic irreducible R-groups. To a certain extent it generalizes the …

… were proved for zero-symmetric near-rings are also valid for arbitrary near-rings. As in the
… construct strongly prime ideals. Matrix near-rings over arbitrary near-rings were introduced …

… Although left near-rings are more frequently used in the literature up to now, we will use right
near-rings: • The left distributive law is in some way unnatural in near-rings of functions (the …