A classification and examples of rank one chain domains

DOI10.1090/S0002-9947-03-03272-0zbMath1037.16023OpenAlexW1930343833MaRDI QIDQ4806456

Hans-Heinrich Brungs, Nikolay Dubrovin

Publication date: 14 May 2003

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-03-03272-0

zbMATH Keywords

total subringsvaluationsgroups of unitsconescovering groupsskew fieldscompletely prime idealslattices of right idealsexceptional chain domains

Mathematics Subject Classification ID

Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Infinite-dimensional and general division rings (16K40) Noncommutative local and semilocal rings, perfect rings (16L30) Ideals in associative algebras (16D25) Units, groups of units (associative rings and algebras) (16U60) Integral domains (associative rings and algebras) (16U10)

Related Items (17)

On central extensions of \(\operatorname{SL}(2,F)\) admitting left-orderings ⋮ Pure projective modules over chain domains with Krull dimension ⋮ Primes of Gauss Extensions Over Crossed Product Algebras ⋮ Annelidan rings ⋮ CLASSIFYING PROJECTIVE MODULES OVER SOME SEMILOCAL RINGS ⋮ Covering classes, strongly flat modules, and completions ⋮ Pure projective modules over exceptional uniserial noncoherent rings. ⋮ Goldie ranks of skew generalized power series rings ⋮ Ziegler spectra of serial rings ⋮ On Annelidan, Distributive, and Bézout Rings ⋮ Gauss extensions and total graded subrings for crossed product algebras. ⋮ Rings with linearly ordered right annihilators ⋮ Rational operators of the space of formal series. ⋮ Uniserial rings of skew generalized power series. ⋮ RightP-Comparable Semigroups ⋮ An indecomposable direct summand of a serial module which is not uniserial ⋮ Primes and Right Ideals in Right Cones

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• π-injective modules and rings whose cyclics are π-injective
• Cones in groups
• A classification of prime segments in simple artinian rings
• Prime Segments of Skew Fields
• Left Valuation Rings and Simple Radical Rings

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