摘要
本文对GB代数作了进一步研究,所得的主要结果为:定理2 设<X;*,e>为GB代数,令G(X)={x_∈X|存在y∈X,使得x=y″},则<G(X);*,e>是群伴代数且(X;*,e>∽<G(X);*,e>.定理4 若<X;*,e>是GB代数,令B(X)={x∈X|x″=e},那么<X/～;*,B(X)>为群伴代数且<X;*,e>∽<X/～;*,B(X)>,这里Vx,y∈X,x～y当且仅当x*y,y*x∈B(X).
In this paper, GB-algebra has been developed. The following theorems were proved:Theorem 1 Let <X; * , e> be a GB-algebra, G(X) = {x∈ X| y∈ X s. t. x =y'}, then <G(X); * , c > be a group-adjoint algebra, and (X; *, e)∽<G(X);*,e>.Theorem 2 If (X; *, e) be a GB-algebra, B(X) = {x∈X|x'=e}, then <X/-; *, B(X)> be a group-adjoint algebra, and <X; *, e>∽(X/-; *, B(X)>,where x,y∈X, x-y x*y, y*x∈B(X).
出处
《西南师范大学学报（自然科学版）》
CAS
CSCD
1991年第2期177-182,共6页
Journal of Southwest China Normal University(Natural Science Edition)
关键词
GB代数
群伴代数
BCI-代数
同态
GB-algebra
group-adjoint algebra
BGI-algebra
homomorphism
quotient algebra
