Characterizing minimal ring extensions

DOI10.1216/RMJ-2011-41-4-1081zbMath1237.13018OpenAlexW2094538883MaRDI QIDQ635260

Thomas G. Lucas, David E. Dobbs, Paul-Jean Cahen

Publication date: 19 August 2011

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmj-2011-41-4-1081

zbMATH Keywords

complete ring of quotientsdense idealminimal ring extensiontotal quotient ringKaplansky ideal transformregular idealring of finite fractionssemiregular idealvaluation pair

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Ideals and multiplicative ideal theory in commutative rings (13A15) Extension theory of commutative rings (13B02) Integral dependence in commutative rings; going up, going down (13B21) Rings of fractions and localization for commutative rings (13B30)

Related Items (12)

Pointwise minimal extensions ⋮ Valuative rings ⋮ Maximal subrings of classical integral domains ⋮ Paul-Jean Cahen (1946–2019) ⋮ Valuative Marot Rings ⋮ Unnamed Item ⋮ THE FERRAND-OLIVIER CLASSIFICATION OF THE MINIMAL RING EXTENSIONS OF A FIELD: A PROOF AND A SURVEY OF ITS INFLUENCE ⋮ On the existence of maximal subrings in commutative noetherian rings ⋮ Finite maximal chains of commutative rings ⋮ Transfer Results for the FIP and FCP Properties of Ring Extensions ⋮ Where Some Inert Minimal Ring Extensions of a Commutative Ring Come from ⋮ Commutative rings with infinitely many maximal subrings

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