On flat overrings, ideal transforms and generalized transforms of a commutative ring

DOI10.1016/0021-8693(71)90058-5zbMath0218.13019OpenAlexW1978533078MaRDI QIDQ2546542

Publication date: 1971

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

Full work available at URL: https://doi.org/10.1016/0021-8693(71)90058-5

Mathematics Subject Classification ID

Integral domains (13G05) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Extension theory of commutative rings (13B02) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Injective and flat modules and ideals in commutative rings (13C11) Rings of fractions and localization for commutative rings (13B30)

Related Items (41)

ON A CLASS OF PRUFER -MULTIPLICATION DOMAINS ⋮ GENERALLY t-LINKATIVE DOMAINS ⋮ How far is a Mori domain from being a Krull domain ? ⋮ Relarively prüfer pairs ⋮ NAGATA TRANSFORMS AND LOCALIZING SYSTEMS ⋮ Module-Theoretic Characterizations of Generalized GCD Domains ⋮ The class group of a strongly mori domain ⋮ Integral domains issued from associated primes ⋮ Prüfer v-multiplication domains and the ring \(R[X_{N_ v}\)] ⋮ Domains of KRULL Type and Ideal Transforms ⋮ Coherent mori domains and the principal ideal theorem ⋮ The S-transform and the ideal transform ⋮ Domains of KRULL Type and Ideal Transforms ⋮ On the ideal class group of a flat overring ⋮ Noetherian-like properties and zero-dimensionality in some extensions of rings ⋮ Agreeable domains ⋮ Generalized Quotient Rings ⋮ Some results on nonnil-multiplication rings ⋮ Invertibility, Semistar Operations, and the Ring of Finite Fractions ⋮ Rings of very strong finite type ⋮ Nonnil-Noetherian rings and the SFT property ⋮ Unnamed Item ⋮ The \(D + E[\varGamma^*\) construction from Prüfer domains and GCD-domains] ⋮ THE v-OPERATION IN EXTENSIONS OF INTEGRAL DOMAINS ⋮ Integral Closure of Generalized Quotient Rings ⋮ Krull rings with zero divisors ⋮ t-splitting multiplicative sets of ideals in integral domains ⋮ Localization and invariant theory ⋮ Star operations in extensions of integral domains ⋮ Intersections d'anneaux intégres ⋮ π-domains, overrings, and divisorial ideals ⋮ Minimal Overrings of an Integrally Closed Domain ⋮ The \(A + X B [X\) construction from Prüfer \(v\)-multiplication domains] ⋮ Star Operations on Overrings and Semistar Operations ⋮ Star-Operations that Distribute Over Finite Intersections ⋮ Modules injective with respect to primes ⋮ The transform formula for ideals ⋮ The \(S\)-transform and its dual with applications to Prüfer extensions ⋮ Finitely generated intermediate rings ⋮ On overrings of strong Mori domains ⋮ Universal property of the Kaplansky ideal transform and affineness of open subsets

Cites Work

This page was built for publication: On flat overrings, ideal transforms and generalized transforms of a commutative ring