【摘要】 <正> [1]决定了具有 n(n≥2)个零因子且元数为 n~2的有限交换环的结构,本文考查代数的情形,将元数换成极大无关组所含元素的个数,决定相应的代数的结构.设 F 是特征零的域,K 是 F 上 n 次扩域,命A={(a,b)|a,b∈K},规定 A 的纯量乘法、加法、乘法分别为:α(a,b)=(αa,αb),Aα∈F,(a,b)+(c,d)=(α+c,b+d),(a,b)·(c,d)=(ac,ad+bc),更多还原

【Abstract】 In this note,the following theorem is proved:LetA be a commutative algebra over a field F.D is the set of all zero divisors of A,and there are n(n≥1)elements of D,which are linearly independent over F,and any n+1 elements of Dare linearly dependent,then,dim_F A≥2n;dim_F A=2n if and only if A is isomorphic to the following algebra B: B={(a,b)|a,b∈K} a(a,b)=(αa,ab) (a,b)+(c,d)=(a+c,b+d) (a,b)·(c,d)=(ac,ad+bc) where K is an extension field of F with(K:F)=n.更多还原