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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Some countability conditions on commutative ring extensions

Authors: Robert Gilmer and William Heinzer
Journal: Trans. Amer. Math. Soc. 264 (1981), 217-234
MSC: Primary 13B02
MathSciNet review: 597878
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Abstract: If $ S$ is a finitely generated unitary extension ring of the commutative ring $ R$, then $ S$ cannot be expressed as the union of a strictly ascending sequence $ \{ {R_n}\} _{n = 1}^\infty $ of intermediate subrings. A primary concern of this paper is that of determining the class of commutative rings $ T$ for which the converse holds--that is, each unitary extension of $ T$ not expressible as $ \cup _1^\infty {T_i}$ is finitely generated over $ T$.

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Keywords: Finitely generated ring extension, Noetherian spectrum, countably generated ideal, von Neumann regular ring
Article copyright: © Copyright 1981 American Mathematical Society

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