The dominion and separable subalgebras of finitely generated algebras
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- by Dean Sanders PDF
- Proc. Amer. Math. Soc. 48 (1975), 1-7 Request permission
Abstract:
Let $R \subseteq S \subseteq A$ be rings with $R$ commutative, $A$ an $R$-algebra which is finitely generated as an $R$-module by $n$-elements, and $S$ a subalgebra of $A$. Setting ${D_0} = S$ and ${D_i} = \operatorname {Dom} (R,{D_{i - 1}})$ for $i \geqslant 1$, we show that ${D_n} = R$. We use this to show that if $S$ is a separable $R$-algebra then $S$ is also finitely generated as an $R$-module. Finally, a characterization of $S$ is given when $A$ is commutative and $S$ is an inertial subalgebra of $A$.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 48 (1975), 1-7
- MSC: Primary 16A16
- DOI: https://doi.org/10.1090/S0002-9939-1975-0364331-1
- MathSciNet review: 0364331