Weyl型代数的环论性质

设A是代数闭域k上有单位元1的交换结合代数，D是A的交换κ-导子组成的非零k-向量空间，苏育才与赵开明引进Weyl型代数AD]并且证明了结合代数AD]是单代数当且仅当A是D-单的且k1D]在A上的作用为忠实的,通过证明AD]与smash product A#U(D)同构，我们给出了这一结果的一个纯环论的证明，同时给出了AD]的一个Ore扩张实现。

Ring Theoretical Properties of Weyl Type Algebras

Let A be a commutative associative algebra with an identity 1 over an algebraically closed field k and D a nonzero k-vector space of commuting k-derivations of A.Su Yucai and Zhao Kaiming introduced the Weyl type algebra AD] and proved that AD],as an associative algebra, is simple if and only if A is D-simple and k1 D] acts faithfully on A. We give a pure ring theoretical proof for this result by proving there is an isomorphism between AD] and the smash product A#U(D). Then we give an Ore extension realization of AD].