Different Prime R-Ideals

Juglal, S.; Groenewald, N. J.; Lee, K. S. E.

doi:10.1142/s1005386710000830

Cited by 7 publications

(4 citation statements)

References 4 publications

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“…• P is c-prime. Proposition 2 ( Juglal et al 2010, Taşdemir et al 2011 If Pv N Γ is c-prime(equiprime), then (P:Γ)vN is c-prime(equiprime). Proposition 3 (Taşdemir et al 2011) If N is RP, Γ is monogenic and (P:Γ)vN is equiprime, then Pv N Γis equiprime.…”

Section: Introductionmentioning

confidence: 98%

“…Veldsman (1992) has examined equiprimeness in depth. Juglal et al (2010) generalized the various notions of primeness (0-, 1-, 2-, 3-, c-primeness) that were defined in a near-ring to the near-ring module. Tasdemir et al (2011) added to these five types by introducing equiprime N-ideals. N is said to be a right permutable (RP) near-ring if abc = acb for all a,b,c ∈N (Birkenmeier and Heatherly 1989).…”

Section: Introductionmentioning

confidence: 99%

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Taşdemir¹

2018

KSEJ

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Then they have studied 3-primeness and c-primeness in details (Taşdemir et al. 2013). In this study, the concept of completely equiprime N-group is generalized to ideals of N-groups, called completely equiprime N-ideals. Also the interconnections of completely equiprime, equiprime and completely prime N-ideals are considered. Furthermore, some relationships between a completely equiprime N-ideal P and the ideal (P: Γ) are obtained. The relation between the concepts of completely equiprime N-ideal and IFP N-ideal is also observed. 2. Preliminaries Throughout this study N stands for a right near-ring. In Pilz's book (1983), for all undefined concepts concerning near-rings are given. For further information in near-rings of prime ideals could be found from Atagün (2010) and Dheena et al. (2004).

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Taşdemir¹

2018

KSEJ

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“…Bhavanari et.al [6] proved the correspondence between the prime left ideals of N and that of M n (N) . Juglal et.al [7] studied different prime N-ideals and prime relations between generalized matrix nearring and multiplication modules over a nearring. Further, Juglal and Groenewald [8] studied the class of strongly prime nearring modules and shown that it forms a -special class.…”

Section: Introductionmentioning

confidence: 99%

Generalization of prime ideals in $$M_n(N)$$-group $$N^{n}$$

Tapatee

Kedukodi

Juglal

et al. 2021

Rend. Circ. Mat. Palermo, II. Ser

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The notion of a matrix nearring over an arbitrary nearring was introduced by (Meldrum and Walt Arch. Math. 47(4): 312–319, 1986). In this paper, we define the notions such as weakly $$\tau$$ τ -prime $$(\tau =0,c,3,e)$$ ( τ = 0 , c , 3 , e ) ideals of an N-group G, which are the generalization of the classes of $$\tau$$ τ -prime ideals of G, and provide suitable examples to distinguish between the two classes. We extend the concept to obtain the one-one correspondence between weakly $$\tau$$ τ -prime ideals $$(\tau =0,c,3,e)$$ ( τ = 0 , c , 3 , e ) of N-group (over itself) and those of $$M_n(N)$$ M n ( N ) -group $$N^{n}$$ N n , where $$M_n(N)$$ M n ( N ) is the matrix nearring over the nearring N. Further, we prove the correspondence between weakly 2-absorbing ideals of these classes.

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“…Recall that modules over near rings are a generalization of near rings. In 2010, Groenewald, Juglal and Lee [7] extended prime ideals of near rings to prime Rideals of modules over near rings.…”

Section: Of Modules Over Near Ringsmentioning

confidence: 99%

2-Absorbing R-ideals of modules over near rings

Patlertsin

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It is known that near rings and modules over near rings are generalized algebraic structures of rings and modules over rings, respectively. In this thesis, we introduce the concepts of 2-absorbing R-ideals of modules over near rings and 2-absorbing ideals of near rings which are generalization of prime R-ideals of modules over near rings and prime ideals of near rings, respectively. Moreover, we present some results analogous to those in ring theory. We provide the notions of strongly 2- absorbing R-ideals of modules over near rings and strongly 2-absorbing ideals of near rings and study some of their properties. Finally, we also focus on some results of 2-absorbing R-ideals of modules over decomposable near rings and 2-absorbing ideals of decomposable near rings.

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Different Prime R-Ideals

Cited by 7 publications

References 4 publications

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Generalization of prime ideals in $$M_n(N)$$-group $$N^{n}$$

2-Absorbing R-ideals of modules over near rings

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