有限生成结合环的局部有限可分性

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2023-03-22 DOI:10.1090/spmj/1751

S. Kublanovskiĭ

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引用次数: 0

摘要

证明了M. Hall定理和N. S. Romanovskii定理的类比在交换环类中是不成立的。建立了单基因环局部有限可分性的充分必要条件。作为推论，证明了有限生成无扭pi环局部有限可分当且仅当其加性群有限生成。

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On the local finite separability of finitely generated associative rings

It is proved that analogs of the theorems of M. Hall and N. S. Romanovskii are not true in the class of commutative rings. Necessary and sufficient conditions for the local finite separability of monogenic rings are established. As a corollary, it is proved that a finitely generated torsion-free PI-ring is locally finitely separable if and only if its additive group is finitely generated.

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.