Primary decomposition of divisorial ideals in Mori domains

DOI10.1016/0021-8693(88)90110-XzbMath0675.13002MaRDI QIDQ1121946

Thomas G. Lucas, T. M. Viswanathan, Evan G. jun. Houston

Publication date: 1988

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

zbMATH Keywords

ascending chain conditionMori domaindivisorial irreducibilitydivisorial primary decompositions

Mathematics Subject Classification ID

Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15) Divisibility and factorizations in commutative rings (13A05) Chain conditions, finiteness conditions in commutative ring theory (13E99)

Related Items (23)

GENERALLY t-LINKATIVE DOMAINS ⋮ When Is (K + I,K[y₁,…,y_t) a Mori Pair?] ⋮ Group rings and semigroup rings over strong Mori domains. II. ⋮ Intersection of powers of prime ideals in krull domains ⋮ Domains with the radical trace property and their complete integral closure ⋮ The class group of a strongly mori domain ⋮ Relations between localizations and \(I\)-adic completions in commutative domains ⋮ Characterizing maximal non-Mori subrings of an integral domain ⋮ On ideals v-generated by two elements ⋮ Various properties of a general class of integer-valued polynomials ⋮ On \(t\)-dimension over strong Mori domains ⋮ On the prime spectrum of a mori domain ⋮ On w-modules over strong mori domains ⋮ Integral domains in which any two \(v\)-coprime elements are comaximal ⋮ Right Mori Orders ⋮ Star-operations induced by overrings ⋮ Group rings and semigroup rings over strong Mori domains. ⋮ w-Divisoriality in Polynomial Rings ⋮ On \(n\)-absorbing ideals of locally divided commutative rings ⋮ Atoms in quasilocal integral domains and Cohen–Kaplansky domains ⋮ Mori domains of integer-valued polynomials ⋮ Factorization in integral domains ⋮ Factorial domains not satisfying the krull intersection property

Cites Work

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• How far is a Mori domain from being a Krull domain ?
• Idéaux divisoriels d'un anneau de polynômes
• The Laskerian property in commutative rings
• On finite conductor domains
• On a class of mori domains
• Coherent mori domains and the principal ideal theorem
• On divisorial ideals in polynomial rings over mori domains

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