【摘要】 每一个子空间都是子代数的代数叫HB-代数。本文讨论了A是HB-代数当且仅当A是下列形式的代数:(一)零乘代数;(二)一维幂等代数Fe;(三)A=Fe+D是向量空间的直和,乘法表有两种,1) e~2=e,D~2=0,eD=0,(?)d∈D,de=d;2) e~2=e,D~2=0,De=0,(?)d∈D,ed=d;(四)B=sum from i(?)I+Fe_i,是向量空间的直和,乘法表有两种,1) (?)k,l∈I,e_k·e_l=e_k·2) (?)k,l∈I,e_ke_l=e_l;(五) A=B+D是向量空间的直和,A的乘法表有两种,D~2=0,1) B的乘法表为e_ke_l=e_k时,A的乘法表为e_iD=0,de_i=d,(?)i∈I,(?)d∈D;2) 当B的乘法表为e_ke_l=e_l时,A的乘法表是De_i=0,e_id=d,(?)i∈I,(?)d∈D。更多还原

【Abstract】 The algebra in which every subspace is a subalgebra is called as HB- algebra. In this paper, we have discussed that A is HB-algebra if and only if A are algebras in following forms:Ⅰ. Zeroalgebra.Ⅱ. One-dimensional power equal algebra (Fe). Ⅲ. "A=Fe■D" is a direct sum of the vecter space where multiplication table has two forms as 1) e~2=e, D~2=0, eD=0, ■d∈D, de=d; 2) e~2=e, D~2=0, De=0, ■d∈D, ed= d; Ⅳ. B = sum from i■I ■ Fe_i, is a direct sum of the vecter space where multiplication has two forms: 1) ■k, l∈I, e_Ke_l=e_k; 2) ■k, l∈I, e_ke_i=e_l.■.A=B■D is a dircct sum of the vecter space where multiplication table has two forms: 1) when the muliplication tables of B and D are e_ke_l=e_k and D~2=0 the multiplication table of A is e_iD=0, de_l=d, ■i∈I, ■d∈D; 2) when the multplication table orb and D are e_ke_l=e_l, and D~2=0, the multiplication table era is De_i=0, e_id=d■i∈I, ■d∈D.更多还原