双交换代数簇的Noetherianity和Specht问题
Noetherianity and Specht problem for varieties of bicommutative algebras
摘要：
满足多项式恒等式x（yz）=y（xz）和（xy）z=（xz）y的非结合代数称为双交换代数。我们证明了如下结果：（i）连续生成的双交换代数是弱Noether代数，即，满足双边理想的升链条件。(ii)本文给出了任意特征域上双交换代数簇的Specht问题（或有限基问题）的正解。
英文摘要：
Nonassociative algebras satisfying the polynomial identities x(yz)=y(xz) and (xy)z=(xz)y are called bicommutative. We prove the following results: (i) Finitely generated bicommutative algebras are weakly noetherian, i.e., satisfy the ascending chain condition for two-sided ideals. (ii) We give the positive solution to the Specht problem (or the finite basis problem) for varieties of bicommutative algebras over an arbitrary field of any characteristic.
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