• 대한수학회지
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• 제42권6호
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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.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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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.

• Korean Journal of Mathematics
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• 제16권3호
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• pp.281-290
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• 2008

The purpose of this paper, GM modules are defined as a generalization of AGR rings. Also, from the faithful GM-property, we get a commutativity of rings. Finally, for a nearring R, we will introduce MR groups, and also derive some properties of GM modules and MR groups.