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- W2300280657 abstract "This paper is a continuation of work done by the present author to- gether with P. R. Hall (1). We characterise the prime and equiprime radicals of N0(G) for certain topological groups G. Various results are obtained concerning primeness and strongly primeness for the sandwich near-ring N0(G,X, ). MSC 2000: 16Y30, 22A05 1. Preliminaries In this paper, all near-rings will be right distributive. All of the near-rings considered in this paper will also be zero-symmetric, that is x0 = 0 for all x 2 (The identity 0x = 0 follows of course from the right distributivity.) The notation C N means is an ideal of N. We refer to Pilz (12) for all undefined concepts concerning near-rings. It is well-known (cf. McCoy (11)) that there are a number of equivalent definitions for primeness in associative rings. These definitions do not coincide for zero-symmetric near- rings. Consequently, a number of generalisations of primeness have appeared in the liter- ature of near-rings. The classical notion is given in (12): A near-ring is called prime (resp. semiprime) if A,B C (resp. A C N), AB = 0 implies A = 0 or B = 0 (resp. A 2 = 0 implies A = 0). is called 3-prime (resp. 3-semiprime) if x,y 2 (resp. x 2 N) xNx = 0 implies x = 0 or y = 0 (resp. xNy = 0 implies x = 0). An ideal I of is called prime (resp. 3-prime) if the factor near-ring N/I is prime (resp. 3-prime). A radical map is a mapping which assigns to evey near-ring an ideal (N) of such that (i) if f : ! R is a surjective near-ring homomorphism, then f( (R)) (S) and (ii) (N/ (N)) = 0 for every near-ring If in addition (iii) ( (N)) = (N) and (iv) I C N," @default.
- W2300280657 created "2016-06-24" @default.
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- W2300280657 date "2005-01-01" @default.
- W2300280657 modified "2023-09-27" @default.
- W2300280657 title "Primeness in Near-rings of Continuous Functions 2" @default.
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