Divisibility Properties of Graded Domains

DOI10.4153/CJM-1982-013-3zbMath0437.13001OpenAlexW2319653993MaRDI QIDQ3877779

David F. Anderson, Daniel D. Anderson

Publication date: 1982

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4153/cjm-1982-013-3

zbMATH Keywords

divisibility graded Krull domains graded GCD-domains graded pi-domains graded UFD properties of graded domains

Mathematics Subject Classification ID

Integral domains (13G05) Graded rings and modules (associative rings and algebras) (16W50) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Divisibility and factorizations in commutative rings (13A05) Chain conditions, finiteness conditions in commutative ring theory (13E99)

Related Items (49)

GRADED w-NOETHERIAN MODULES OVER GRADED RINGS ⋮ The Schreier property and the composite semigroup ring A + B[Γ*] ⋮ General w-ZPI-Rings and a Tool for Characterizing Certain Classes of Monoid Rings ⋮ Group rings and semigroup rings over strong Mori domains. II. ⋮ On graded coherent-like properties in trivial ring extensions ⋮ Graded integral domains which are UMT-domains ⋮ On the \(S\)-class group of the monoid algebra \(D[\Gamma\)] ⋮ Graded almost pseudo-valuation domains ⋮ Primality in Semigroup Rings ⋮ \(Gr\)-injective modules and \(gr\)-projective modules over \(G\)-graded commutative rings ⋮ Graded pseudo-valuation domains ⋮ UMT-domains: A Survey ⋮ Noetherian properties in monoid rings. ⋮ Graded integral domains and Nagata rings ⋮ Primitive localizations of an enveloping algebra ⋮ Divisorial ideals and invertible ideals in a graded integral domain ⋮ Graded integral domains in which each nonzero homogeneous t-ideal is divisorial ⋮ GRADED INTEGRAL DOMAINS IN WHICH EACH NONZERO HOMOGENEOUS IDEAL IS DIVISORIAL ⋮ Root closure in integral domains ⋮ Characterizations of graded Prüfer \(\star \)-multiplication domains. II ⋮ UMT-domain property in pullbacks of graded integral domains ⋮ Graded Prüfer domains ⋮ Graded almost valuation domains ⋮ Factorial domains and graded rings ⋮ WHEN ARE GRADED INTEGRAL DOMAINS ALMOST GCD-DOMAINS ⋮ Discrete valuation overrings of a graded Noetherian domain ⋮ Prüfer domains and graded rings ⋮ Homogenization and dimension in Λ - graded rings ⋮ When graded domains are Schreier or pre-Schreier ⋮ Homogeneous splitting sets of a graded integral domain ⋮ Integral Closure of Graded Integral Domains ⋮ Group rings and semigroup rings over strong Mori domains. ⋮ Graded Prüfer domains with Clifford homogeneous class semigroups ⋮ Radical factorization in finitary ideal systems ⋮ CHARACTERIZATIONS OF GRADED PRÜFER ⋆-MULTIPLICATION DOMAINS ⋮ Divisibility properties of twisted semigroup rings ⋮ The Semicenter of an Enveloping Algebra is Factorial ⋮ Graded-valuation domains ⋮ A Note on the Dimension Theory of ℤⁿ-Graded Rings ⋮ The space of homogeneous preserving semistar operations on graded domains ⋮ The distribution of prime divisors in Krull monoid domains ⋮ Unique factorization of ideals in commutative rings with zero divisors ⋮ Graded powerful ideals in a graded integral domain ⋮ Some Results on Factorization in Integral Domains ⋮ Graded Rings and Krull Orders ⋮ Semigroup algebras and direct sums of domains ⋮ On graded pseudo-valuation domains ⋮ On the class group of a graded domain ⋮ A characterization of graded pseudo-valuation domains

This page was built for publication: Divisibility Properties of Graded Domains