一类非结合泛代数的次直积分解

本文引入一类非结合泛代数，即零积结合近环，研究其次直积分解，得到两个结构定理。设Ｎ是零积结合分配生成近环，本文证明了：（ｉ）如果Ｎ是次直不可约的且无非零的二次幂零元，则Ｎ是整的；（ｉｉ）Ｎ是零积结合分配生成整近环的次直积当且仅当Ｎ不含非零的二次幂零元。这些结果在这一类泛代数中加强了著名的Ｂｉｒｋｈｏｆｆ定理。

The Subdirect Product Decomposition of a Class of Nonassociative Universal Algebras

In this paper a class of nonassociative universal algebras,i, e.,zero-product-associative near-rings is introduced and their subdirect product decomposi-tions are studied.Two structure theorems are obtained.Suppose that N is a zero-product-associative distributively generated near-ring,it is shown that(i) if N is a subdirectly irreducible and has no nonzero nilpotent element of index 2,then N is integral,and(ii) N is a subdirect product of zero-product-associative distributively generated near-rings if and only if N has no nonzero nilpotent element of index 2. These results improve the famous Birkhoff Theorem for the class of universal alge-bras.