|
Research Papers
On local finite separability of finitely generated associative rings
S. I. Kublanovskii ТПО «Северный Очаг» Санкт-Петербург, Россия
Abstract:
It is proved that analogs of the theorems of M. Hall and N. S. Romanovsky fail in the class of commutative rings. Necessary and sufficient conditions for local finite separability of monogenic rings is 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.
Keywords:
finite pproximation, occurrence in a subring, monogenic ring, commutative ring, closedness in the profinite topology.
Received: 09.08.2021
Citation:
S. I. Kublanovskii, “On local finite separability of finitely generated associative rings”, Algebra i Analiz, 34:2 (2022), 95–117; St. Petersburg Math. J., 34:2 (2023), 205–220
Linking options:
https://www.mathnet.ru/eng/aa1802 https://www.mathnet.ru/eng/aa/v34/i2/p95
|
Statistics & downloads: |
Abstract page: | 275 | Full-text PDF : | 3 | References: | 41 | First page: | 38 |
|