Almost Splitting Sets and AGCD Domains

DOI10.1081/AGB-120027857zbMath1063.13002OpenAlexW2067120444MaRDI QIDQ4454161

Tiberiu Dumitrescu, Muhammad Zafrullah, Daniel D. Anderson

Publication date: 7 March 2004

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

Full work available at URL: https://doi.org/10.1081/agb-120027857

zbMATH Keywords

integral domainintegral closurealmost GCD domaingoing uproot extensionAGCD domain

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Polynomials over commutative rings (13B25) Ideals and multiplicative ideal theory in commutative rings (13A15) Divisibility and factorizations in commutative rings (13A05)

Related Items (13)

Numerical Semigroup Rings and Almost Prüferv-Multiplication Domains ⋮ On Almost Prüfer v-Multiplication Domains ⋮ Almost splitting sets in integral domains. II ⋮ ∗-Almost super-homogeneous ideals in ∗-h-local domains ⋮ Nagata-like theorems for almost Prüfer \(v\)-multiplication domains ⋮ On locally AGCD domains ⋮ Root extension in polynomial and power series rings ⋮ WHEN ARE GRADED INTEGRAL DOMAINS ALMOST GCD-DOMAINS ⋮ Almost splitting sets in integral domains ⋮ 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
• The \(D+XD_ s[X\) construction from GCD-domains]
• Some remarks on star-operations
• Almost Bézout domains
• Splitting the t-class group
• The construction \(D+XD_s[X\)]
• Splitting sets in integral domains
• LCM-splitting sets in some ring extensions
• Atomic domains in which almost all atoms are prime
• Convex Directed Subgroups of a Group of Divisibility
• Almost GCD domains of finite \(t\)-character.

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