• Title/Summary/Keyword: AGR rings

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R-HOMOMORPHISMS AND R-HOMOGENEODS MAPS

  • Cho, Yong-Uk
    • 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.

A STUDY ON R-GROUPS WITH MR-PROPERTY

  • CHO YONG UK
    • 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.

SOME PROPERTIES OF GM MODULES AND MR GROUPS

  • Cho, Yong Uk
    • Korean Journal of Mathematics
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    • v.16 no.3
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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.

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