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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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참고문헌 (25)
참고문헌 신청
C. Huh / 2005 / Basic examples and extensions of symmetric rings / J. Pure Appl. Algebra 202 (1-3) : 154 ~ 167
C. P. Milies / 2002 / An Introduction to Group Rings / Kluwer Academic Pub-lishers
E. H. Feller / 1958 / Properties of primary noncommutative rings / Trans. Amer. Math. Soc 89 : 79 ~ 91
G. Marks / 2002 / Reversible and symmetric rings / J. Pure Appl. Algebra 174 (3) : 311 ~ 318
G. Shin / 1973 / Prime ideals and sheaf representation of a pseudo symmetric ring / Trans. Amer. Math. Soc 184 : 43 ~ 60
C. P. Milies / 2002 / An Introduction to Group Rings / Kluwer Academic Pub-lishers
E. H. Feller / 1958 / Properties of primary noncommutative rings / Trans. Amer. Math. Soc 89 : 79 ~ 91
G. Marks / 2002 / Reversible and symmetric rings / J. Pure Appl. Algebra 174 (3) : 311 ~ 318
G. Shin / 1973 / Prime ideals and sheaf representation of a pseudo symmetric ring / Trans. Amer. Math. Soc 184 : 43 ~ 60
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