论文标题
圈子定理的仿射性代表性和决策程序的戒指和代数
Affine representability and decision procedures for commutativity theorems for rings and algebras
论文作者
论文摘要
我们考虑了Affine Odanity定理的一个限制版本的应用，该定理遵循Belov-Kanel，Rowen和Vishne的最新作品。使用此结果，我们能够证明，当给定一组有限的多项式身份时，有一种算法在有限数量的步骤后终止，这些步骤决定这些身份是否迫使一个环为交换。然后，我们根据这种算法重新审视雅各布森和赫斯坦的旧换向定理，并在这种静脉中获得一般结果。此外，我们完全表征了暗示环的通勤性的均匀多线性身份。
We consider applications of a finitary version of the Affine Representability theorem, which follows from recent work of Belov-Kanel, Rowen, and Vishne. Using this result we are able to show that when given a finite set of polynomial identities, there is an algorithm that terminates after a finite number of steps which decides whether these identities force a ring to be commutative. We then revisit old commutativity theorems of Jacobson and Herstein in light of this algorithm and obtain general results in this vein. In addition, we completely characterize the homogeneous multilinear identities that imply the commutativity of a ring.
