Some Study on Morphic Ring
Chu Mao-quan
Abstract
Chu Mao-quan
Abstract
In this paper,we mainly depicted the relation of morphic ring and other rings under certain conditions.We mainly proved the following results: 1.If R is a left quasi-duo ring,and R is a GP-V-ring,then R is a morphic ring;2.If R is a left GP-V-ring,the following conditions are equivalent,(1) R is a strongly regular ring;(2) R is a reduced morphic ring;(3) R is a semicommutative morphic ring;(4) R is a 2-primal morphic ring.
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In this paper,we mainly depicted the relation of morphic ring and other rings under certain conditions.We mainly proved the following results: 1.If R is a left quasi-duo ring,and R is a GP-V-ring,then R is a morphic ring;2.If R is a left GP-V-ring,the following conditions are equivalent,(1) R is a strongly regular ring;(2) R is a reduced morphic ring;(3) R is a semicommutative morphic ring;(4) R is a 2-primal morphic ring.
Key concepts: Ring (chemistry), Reduced ring, Simple ring, Primitive ring, Mathematics, Boolean ring, Principal ideal ring, Discrete mathematics