Almost splitting sets in integral domains

DOI10.1016/J.JPAA.2004.08.035zbMath1091.13001OpenAlexW2037273473MaRDI QIDQ1772258

Gyu Whan Chang

Publication date: 18 April 2005

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2004.08.035

zbMATH Keywords

class groupintegral domainAGCD-domainalmost splitting set

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Divisibility and factorizations in commutative rings (13A05)

Related Items (11)

Almost splitting sets in integral domains. II ⋮ Nagata-like theorems for almost Prüfer \(v\)-multiplication domains ⋮ Integral domains of finite \(t\)-character ⋮ WHEN ARE GRADED INTEGRAL DOMAINS ALMOST GCD-DOMAINS ⋮ Prüfer \(v\)-multiplication domains and related domains of the form \(D+D_S[\varGamma ^{*}\)] ⋮ Studying monoids is not enough to study multiplicative properties of rings: an elementary approach. ⋮ On the set of \(t\)-linked overrings of an integral domain ⋮ Almost Prüferv-Multiplication Domains and Related Domains of the FormD + D_S[Γ*] ⋮ A General Theory of Almost Splitting Sets ⋮ t-SPLITTING SETS S OF AN INTEGRAL DOMAIN D SUCH THAT D_SIS A FACTORIAL DOMAIN ⋮ ALMOST SPLITTING SETS S OF AN INTEGRAL DOMAIN D SUCH THAT D_SIS A PID

Cites Work

• A general theory of almost factoriality
• Prüfer v-multiplication domains and the ring \(R[X_{N_ v}\)]
• Almost Bézout domains
• Splitting the t-class group
• The class group of integral domains.
• \(t\)-splitting sets in integral domains.
• On the class group of a pullback
• On the class group and the local class group of a pullback
• Weakly Krull and related domains of the form \(D+M, A+XB[X\) and \(A+X^2B[X]\)]
• Splitting sets in integral domains
• LCM-splitting sets in some ring extensions
• t-Linked overrings and prüfer v-multiplication domains
• On t-invertibility II
• On divisorial ideals in polynomial rings over mori domains
• Almost Splitting Sets and AGCD Domains
• Almost GCD domains of finite \(t\)-character.
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