Topologically defined classes of going-down domains

Papick, Ira J.

doi:10.1090/S0002-9947-1976-0401745-0

Topologically defined classes of going-down domains
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by Ira J. Papick PDF

Trans. Amer. Math. Soc. 219 (1976), 1-37 Request permission

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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