每一个子代数都是半理想的代数  

THE ALGEBRA IN WHICH EVERY SUBALGEBRA IS SEMI—IDEAL

作　　者：吕海波[1] 李文深[1] 罗嗣卿[1] 程思坦 

机构地区：[1]东北林业大学,大庆供电公司

出　　处：《东北林业大学学报》1993年第5期111-114,共4页Journal of Northeast Forestry University

摘　　要：讨论A是H—代数当且仅当A是下列形式的代数:(一)一维幂等代数;(二)B是幂零元代数;(三)A=<e>+B;(四)A=<e>+A_1(向量空间直和),且A_1~2=0,(?)a∈A_1,ea=a,ae=0;(五)A=<e>+A_2(向量空间直和)且A_2~2=0,(?)a∈A_2,ae=0,ea=a;(六)A=<e>+A_1+B(向量空间直和),(?)a∈A_1,b∈B,ab=ba=0,(?)b_1∈B,(?)b∈B,有b_1b=βb^2;(七)A=<e>+A_2+B乘法表为,(?)a∈A_2,(?)b∈B,ab=ba=0,且(?)b_1,b∈B有bb_1=βb^2。This paper has discussed that A is H—algebra if A is the algebra with following forms. Ⅰ. one—dimensional power equal algebra. Ⅱ. The power zero-element exponent ≤3,when ab≠0,ba≠0,ab=a_1 a^2 or ba=a^2 a^2;Ⅲ.A=<e>+Be; Ⅳ. A=<e>+A_1 A_1~2=0,(?)a∈A_1,ea=a, ae=0;V.A=<e>+A_2,A_2~2=0,(?)a∈A_2, ea=0, ae=a;Ⅵ. A=<e>+A_1+Be, (?)a∈A_1, (?)b∈Be, ab=ba=0,(?)b_1, b∈B, b_1b=βb^2, Ⅶ. A=<e>+A_2+B, (?)a∈A_2, (?)b∈B, ab=ba=0, (?)b_1, b∈B, bb_1=βb^2.

关 键 词：结合代数 半理想 H-代数 

分 类 号：O153[理学—数学]