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RINGS WITH A FINITE NUMBER OF ORBITS UNDER THE REGULAR ACTION
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 Title & Authors
RINGS WITH A FINITE NUMBER OF ORBITS UNDER THE REGULAR ACTION
Han, Juncheol; Park, Sangwon;
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 Abstract
Let R be a ring with identity, X(R) the set of all nonzero, non-units of R and G(R) the group of all units of R. We show that for a matrix ring , , if a, b are singular matrices of the same rank, then , where and are the orbits of a and b, respectively, under the left regular action. We also show that for a semisimple Artinian ring R such that , , with infinite division rings of the same cardinalities or R is isomorphic to the ring of matrices over a finite field if and only if for all .
 Keywords
left (right) regular action;orbit;left Artinian ring;
 Language
English
 Cited by
1.
UNIT-DUO RINGS AND RELATED GRAPHS OF ZERO DIVISORS, Bulletin of the Korean Mathematical Society, 2016, 53, 6, 1629  crossref(new windwow)
2.
Structure of Abelian rings, Frontiers of Mathematics in China, 2017, 12, 1, 117  crossref(new windwow)
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