On equiprime near-rings

Veldsman, Stefan

doi:10.1080/00927879208824479

Cited by 23 publications

(13 citation statements)

References 13 publications

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“…[25] and Groenewald [9,10]) 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: Introductionmentioning

confidence: 98%

Reference points and roughness

Kedukodi¹,

Kuncham²,

Satyanarayana³

2010

Information Sciences

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Section: Introductionmentioning

confidence: 98%

Reference points and roughness

Kedukodi¹,

Kuncham²,

Satyanarayana³

2010

Information Sciences

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“…The class of equiprime nearrings is well-known in nearrings. An extensive set of examples of equiprime nearrings can be found in Veldsman [17].…”

Section: Preliminary Notesmentioning

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%

Nearring ideals, graphs and cliques

Kedukodi¹,

Prasad²,

Satyanarayana³

2013

imf

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In this paper, we define the notion of fuzzy graph of a nearring N with respect to a level ideal µ t denoted by (N, µ, σ, t). The primary aim of this notion is to depict graphically the fuzzy character which is concealed algebraically in the examples of 3-prime fuzzy ideals of a nearring N . We find that if N is a zero-symmetric nearring and µ is 3-prime fuzzy ideal of N , then (N, µ, σ, t) has a special type of symmetry. We call this symmetry as the ideal symmetry of (N, µ, σ, t). We find the conditions under which the ideal symmetry of (N, µ, σ, t) implies µ is a 3-prime fuzzy ideal of N . Finally, we obtain a result which finds all the fuzzy cliques of (N, µ, σ, t) whenever µ is 3-prime and N is zerosymmetric.Mathematics Subject Classification: 16Y30, 03E72, 16Y99

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“…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%