Generalized Prime Ideals in Non-associative Near-rings I
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In this paper, the concept of ∗-prime ideals in non-associative near-rings is introduced and then will be studied. For this purpose, first we introduce the notions of ∗-operation, ∗-prime ideal and ∗-system in a near-ring. Next, we will define the ∗-sequence, ∗-strongly nilpotent and ∗-prime radical of near-rings, and then obtain some characterizations of ∗-prime ideal and ∗-prime radical r_s(I) of an ideal I of near-ring N.
Abstract
In this paper, the concept of ∗-prime ideals in non-associative near-rings is introduced and then will be studied. For this purpose, first we introduce the notions of ∗-operation, ∗-prime ideal and ∗-system in a near-ring. Next, we will define the ∗-sequence, ∗-strongly nilpotent and ∗-prime radical of near-rings, and then obtain some characterizations of ∗-prime ideal and ∗-prime radical r_s(I) of an ideal I of near-ring N.
참고문헌 (5)
- N. J. Groenewald, "A generalization of prime ideals in near-rings", Comm. in Algebra, 12(15), pp.1835~1853 (1984)
- K. Murata, "A generalization of prime radical in rings", Osaka J. Math, 66, pp.291~301 (1969)
- H. C. Myung, "On prime ideals and primary decomposition in a non-associative rings", Osaka J. Math, 9, pp.41~47 (1972)
- H. C. Myung, "A generalization of prime radical in non-associative rings", Paci c Journal of Mathematics, 42(1), pp.187~193 (1972)
- G. Pilz, "Near-rings" (1983), North Holland Publishing Company