Hai Zhou
Abstract
This paper proves mainly that if is R a right qusi-duo ring whose every singular simple right R-module M is YJ-injective, then (1)if N 1(R) is regular, then R is regular; (2)if N 0(R) is regular, then R is regular; (3)if R is abelian, then R is regular; (4)if N 0(R)C(R),then R is regular.
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This paper proves mainly that if is R a right qusi-duo ring whose every singular simple right R-module M is YJ-injective, then (1)if N 1(R) is regular, then R is regular; (2)if N 0(R) is regular, then R is regular; (3)if R is abelian, then R is regular; (4)if N 0(R)C(R),then R is regular.
Key concepts: Mathematics, Injective function, Simple (philosophy), Regular ring, Combinatorics, Abelian group, Von Neumann regular ring, Ring (chemistry)