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2004•Unpublished venueRequires access

Some Characterizations on Strongly Regular Rings

F Yin

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Abstract

Let R is a ring,if xy-yx∈C(R),for all x,y∈R,then following statements are equivalent: (1)R is a strongly regular ring,(2)R is a Von Neumann regular ring,(3)R is a generalized regular ring;Let R is a semi commutative ring,then following statements are equivalent:(1)R is a strongly regular ring,(2)Every maximal essential left ideals of R are left GP-injective modules,(3)Every maximal essential right ideals of R are right GP-injective modules.

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What this paper is about

Let R is a ring,if xy-yx∈C(R),for all x,y∈R,then following statements are equivalent: (1)R is a strongly regular ring,(2)R is a Von Neumann regular ring,(3)R is a generalized regular ring;Let R is a semi commutative ring,then following statements are equivalent:(1)R is a strongly regular ring,(2)Every maximal essential left ideals of R are left GP-injective modules,(3)Every maximal essential right ideals of R are right GP-injective modules.

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Available abstract

Let R is a ring,if xy-yx∈C(R),for all x,y∈R,then following statements are equivalent: (1)R is a strongly regular ring,(2)R is a Von Neumann regular ring,(3)R is a generalized regular ring;Let R is a semi commutative ring,then following statements are equivalent:(1)R is a strongly regular ring,(2)Every maximal essential left ideals of R are left GP-injective modules,(3)Every maximal essential right ideals of R are right GP-injective modules.

Key concepts: Von Neumann regular ring, Mathematics, Regular ring, Ring (chemistry), Primitive ring, Commutative ring, Principal ideal ring, Injective function

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