1991
DOI: 10.1080/00927879108824287
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Different prime ideals in near-rings

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Cited by 41 publications
(35 citation statements)
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“…In this section we refer to [1,4,6,7] for some elementary aspects and quote a number of theorems and lemmas that are essential to step up this study. For more details we refer to the papers in the references.…”
Section: Basic Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…In this section we refer to [1,4,6,7] for some elementary aspects and quote a number of theorems and lemmas that are essential to step up this study. For more details we refer to the papers in the references.…”
Section: Basic Resultsmentioning
confidence: 99%
“…In 1988 N.J. Groenewald introduced the notion of completely (semi) prime ideals of a near-ring [3]. In 1991 N.J. Groenewald introduced the notion of 3-(semi) prime ideals of a near-ring [4]. In [5] D.D.…”
Section: Introductionmentioning
confidence: 99%
“…(Veldsman [17] and Groenewald [10,11]) The notions of equiprime ideal, 3-prime ideal and prime ideal coincide in rings. In commutative rings the notions of equiprime ideal, 3-prime ideal, c-prime ideal and prime ideal coincide.…”
Section: Preliminary Notesmentioning
confidence: 99%
“…(Groenewald [11]) An ideal I of N is called 3-prime if a, b ∈ N and arb ∈ I for all r ∈ N implies a ∈ I or b ∈ I.…”
Section: Preliminary Notesmentioning
confidence: 99%
“…But in the class of near-rings, we have R is equiprime implies that R is zero-symmetric 3-prime, R is 3-prime implies R is 2-prime, R is zero-symmetric 2-prime implies R is 1-prime and R is 1-prime implies R is 0-prime. For details see [8], [10], [12], [13] and [19].…”
Section: Throughout This Paper R Is a Left Near-ring And Z(r) Is The mentioning
confidence: 99%