Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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DUO RING PROPERTY RESTRICTED TO GROUPS OF UNITS

  • Han, Juncheol (Department of Mathematics Education Pusan National University) ;
  • Lee, Yang (Department of Mathematics Education Pusan National University) ;
  • Park, Sangwon (Department of Mathematics Dong-A University)
  • Received : 2014.07.10
  • Published : 2015.05.01
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Abstract

We study the structure of right duo ring property when it is restricted within the group of units, and introduce the concept of right unit-duo. This newly introduced property is first observed to be not left-right symmetric, and we examine several conditions to ensure the symmetry. Right unit-duo rings are next proved to be Abelian, by help of which the class of noncommutative right unit-duo rings of minimal order is completely determined up to isomorphism. We also investigate some properties of right unit-duo rings which are concerned with annihilating conditions.

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References

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  1. UNIT-DUO RINGS AND RELATED GRAPHS OF ZERO DIVISORS vol.53, pp.6, 2016, https://doi.org/10.4134/BKMS.b150684