Open Problems in Commutative Ring Theory

DOI10.1007/978-1-4939-0925-4_20zbMath1327.13002OpenAlexW73163491MaRDI QIDQ2949011

Marco Fontana, Paul-Jean Cahen, Sarah Glaz, Sophie Frisch

Publication date: 7 October 2015

Published in: Commutative Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4939-0925-4_20

zbMATH Keywords

gradedensitystable ringfactorizationRees algebragroup ringJaffard domainPrüfer ringhomological dimensionsinteger-valued polynomialsoverringintegral closuresemistar operationstar operationRees valuationmatrix ringfactorialdivided domainPvMDKronecker function ringintegral closure of an idealfinite characterMori domaincomplete ringMcCoy ringspectrum of a ringstraight domainabsorbing idealdivisorial domainlocally tame domain

Mathematics Subject Classification ID

Homological dimension and commutative rings (13D05) Integral closure of commutative rings and ideals (13B22) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Commutative Noetherian rings and modules (13E05) Valuations and their generalizations for commutative rings (13A18) Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15) Valuation rings (13F30) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15) Divisibility and factorizations in commutative rings (13A05) Research exposition (monographs, survey articles) pertaining to commutative algebra (13-02) Homological methods in commutative ring theory (13D99)

Related Items (max. 100)

The Anderson-Badawi conjecture for commutative algebras over infinite fields ⋮ Module-theoretic characterizations of the ring of finite fractions of a commutative ring ⋮ ∗-Almost super-homogeneous ideals in ∗-h-local domains ⋮ Some topological considerations on semistar operations ⋮ Integer-valued polynomials on valuation rings of global fields with prescribed lengths of factorizations ⋮ The small finitistic dimensions of commutative rings ⋮ Paul-Jean Cahen (1946–2019) ⋮ On Anderson-Badawi conjectures ⋮ Every Prüfer ring does not have small finitistic dimension at most one ⋮ A new semistar operation on a commutative ring and its applications ⋮ On strongly primary monoids and domains ⋮ On n-absorbing and strongly n-absorbing ideals of amalgamation ⋮ n-Absorbing Ideals of Commutative Rings and Recent Progress on Three Conjectures: A Survey ⋮ On the module structure of the integer-valued polynomial rings ⋮ A proof of the Anderson-Badawi \(\operatorname{rad}(I)^n\subseteq I\) formula for \(n\)-absorbing ideals ⋮ Divisorial behavior of prime ideals in Prüfer domains ⋮ Finitistic weak dimensions of pullbacks ⋮ On n-absorbing ideals and (m,n)-closed ideals in trivial ring extensions of commutative rings ⋮ On \(n\)-absorbing ideals of locally divided commutative rings

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