The completely prime radical in near-rings

Groenewald, N. J.

doi:10.1007/bf01903337

Cited by 26 publications

(17 citation statements)

References 3 publications

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“…The equivalence of parts (a) and (b) in the above theorem were noted by GROENF~WALD [16] and REDDY and MURTV [33] for zero symmetric near-rings. However, Example 2.8 will show that the result does not hold for arbitrary near-rings.…”

Section: Lemma 22 Let I Be An Ideal Of R (I) R Is 2-primal If and mentioning

confidence: 75%

“…The intersection of all of the completely prime ideals of R, denoted herein by P2(R), is the completely prime radical of R. (This notation was introduced in [31]. Different notation was used by GROENEWALO [15], [16], wherein he carried out the first major investigation of this radical for near-rings). This paper investigates conditions under which a prime ideal is completely prime and conditions for which every prime ideal in a near-ring is completely prime.…”

Section: Introductionmentioning

confidence: 99%

“…The terminology "completely prime" is now standard in ring theory and is becoming dominant for near-rings. (See [15], [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]). If the zero ideal of R is a completely prime ideal, then we say R is a completely prime near-ring.…”

Section: Introductionmentioning

confidence: 99%

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Prime ideals and prime radicals in near-rings

Birkenmeier

Heatherly

Lee

1994

Monatshefte f�r Mathematik

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Section: Lemma 22 Let I Be An Ideal Of R (I) R Is 2-primal If and mentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

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Prime ideals and prime radicals in near-rings

Birkenmeier

Heatherly

Lee

1994

Monatshefte f�r Mathematik

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“…(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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“…In 1977 G. Pilz introduced the notion of prime ideals of a near-ring [1]. 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].…”

Section: Introductionmentioning

confidence: 99%

Some Basic Properties of Completely Prime Ideals in Near Rings

Yiarayong

2015

j.math.fund.sci.

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Abstract. In this investigation we studied completely prime, weakly completely prime, quasi completely prime and weakly quasi completely prime ideals in near-rings. Some characterizations of completely prime and weakly completely prime ideals were obtained. Moreover, we investigated relationships between completely prime and weakly completely prime ideals in near-rings. Finally, we obtained necessary and sufficient conditions for a weakly completely prime ideal to be a completely prime ideal.

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The completely prime radical in near-rings

Cited by 26 publications

References 3 publications

Prime ideals and prime radicals in near-rings

Prime ideals and prime radicals in near-rings

Nearring ideals, graphs and cliques

Some Basic Properties of Completely Prime Ideals in Near Rings

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