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Transactions of the American Mathematical Society

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



Topologically defined classes of going-down domains

Author: Ira J. Papick
Journal: Trans. Amer. Math. Soc. 219 (1976), 1-37
MSC: Primary 13G05
MathSciNet review: 0401745
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Abstract: Let R be an integral domain. Our purpose is to study GD (going-down) domains which arise topologically; that is, we investigate how certain going-down assumptions on R and its overrings relate to the topological space $ {\text{Spec}}(R)$. Many classes of GD domains are introduced topologically, and a systematic study of their behavior under homomorphic images, localization and globalization, integral change of rings, and the ``$ D + M$ construction'' is undertaken. Also studied, is the algebraic and topological relationships between these newly defined classes of GD domains.

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Keywords: Going-down, treed, mated, open, propen, branch, G-domain, fiber, trunk, vertex
Article copyright: © Copyright 1976 American Mathematical Society

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