Journal of the
Korean Mathematical Society JKMS

We study the structure of right duo ring property when it is restricted within the group of units, and introduce the concept of {\it 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.

Keywords: right unit-duo ring, right duo ring, right unit-duo ring of minimal order, left-right symmetric, annihilator, group ring

MSC numbers: 16U80, 16D25, 16U60, 16W22