• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.303-310
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• 2006

M. $Bre\v{s}ar$ and J. Vukman obtained some results concerning orthogonal derivations in semiprime rings which are related to the result that is well-known to a theorem of Posner for the product of two derivations in prime rings. In this paper, we present orthogonal generalized derivations in semiprime near-rings.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.433-445
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• 2016

In the present paper, we expand the domain of work on the concept of semiderivations in 3-prime near-rings through the study of structure and commutativity of near-rings admitting semiderivations satisfying certain differential identities. Moreover, several examples have been provided at places which show that the assumptions in the hypotheses of various theorems are not altogether superfluous.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.17-26
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• 2019

In this paper, we investigate commutativity of 3-prime near-rings ${\mathcal{N}}$ in which (1, ${\alpha}$)-derivations satisfy certain algebraic identities. Some well-known results characterizing commutativity of 3-prime near-rings have been generalized. Furthermore, we give some examples show that the restriction imposed on the hypothesis is not superfluous.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1153-1167
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• 2005

In this paper, all rings and all near-rings R are associative, all modules are right R-modules. For a near-ring R, we consider representations of R as R-groups. We start with a study of AGR rings and their properties. Next, for any right R-module M, we define a new concept GM module and investigate the commutative property of faithful GM modules and some characterizations of GM modules. Similarly, for any near-ring R, we introduce an R-group with MR-property and some properties of MR groups.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.137-142
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• 2001

In this paper, we initiate the study of some annihilator conditions on polynomials which were used by Kaplansky [4] to abstract algebras of bounded linear operators on a Hilbert spaces with Baer condition. On the other hand, p.p. rings were introduced by A. Hattori [3] to study the torsion theory. The purpose of this paper is to introduce near-rings with Baer condition and near-rings with p.p. condition which are somewhat different from the ring case, and to extend a results of Armendarz [1] to polynomial near-rings with Baer condition in somewhat different way of Birkenmeier and Huang [2].

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.573-583
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• 2005

In this paper, all near-rings R are left near-rings and all representations of R are (right) R-groups. We start with a study of AR, almost AR and AGR rings which are motivated by the works on the Sullivan's Problem [10] and its properties. Next, for any R-group G, we introduce a notion of R-groups with M R-property and investigate their properties and some characterizations of these R-groups. Finally, for the faithful M R-property, we get a commutativity of near-rings and rings.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.3
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• pp.225-229
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• 2006

In this paper, we introduce some concepts of ${\Gamma}$-near-ring and obtain their properties on ${\Gamma}$-near-rings through regularity conditions.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.509-513
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• 2010

In this paper, we will investigate some properties of strongly reduced near-rings. The purpose of this paper is to find more characterizations of the strong regularity in near-rings, which are closely related with strongly reduced near-rings.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.1-7
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• 1997

We characterize fuzzy ideals in near-rings and extensions of such ideals with the sup property.

• The Pure and Applied Mathematics
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• v.13 no.2 s.32
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• pp.157-165
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• 2006

The notion of regularity in near-ring was generalized by the concept of b-regular and some characterizations of the same was obtained through the substructures viz bi-ideals in near-rings. In this paper, we generalize further and introduce tile notion of weakly b-regular near-rings and obtain a characterization of tile same.