Cancellation properties in ideal systems: A classification of e.a.b. semistar operations

DOI10.1016/j.jpaa.2009.03.001zbMath1187.13003arXiv0905.0217OpenAlexW2007752037MaRDI QIDQ1030702

Marco Fontana, K. Alan Loper

Publication date: 2 July 2009

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

Full work available at URL: https://arxiv.org/abs/0905.0217

Mathematics Subject Classification ID

Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15) Valuation rings (13F30) Chain conditions, finiteness conditions in commutative ring theory (13E99)

Related Items (18)

Radical semistar operations ⋮ Towards a classification of stable semistar operations on a Prüfer domain ⋮ Some Closure Operations in Zariski-Riemann Spaces of Valuation Domains: A Survey ⋮ Kronecker function rings and power series rings ⋮ Polynomial extensions of semistar operations ⋮ The sets of star and semistar operations on semilocal Prüfer domains ⋮ On some classes of integral domains defined by Krull's \(a.b.\) operations ⋮ A gg-Cancellative Semistar Operation on an Integral Domain Need Not Be gh-Cancellative ⋮ Some applications of the ultrafilter topology on spaces of valuation domains, Part I ⋮ Some applications of the ultrafilter topology on spaces of valuation domains, Part II ⋮ The upper Vietoris topology on the space of inverse-closed subsets of a spectral space and applications ⋮ An Overring-Theoretic Approach to Polynomial Extensions of Star and Semistar Operations ⋮ New Distinguished Classes of Spectral Spaces: A Survey ⋮ The space of homogeneous preserving semistar operations on graded domains ⋮ Lorenzen Monoids: A Multiplicative Approach to Kronecker Function Rings ⋮ Note on Cancellation Properties in Ideal Systems ⋮ The constructible topology on spaces of valuation domains ⋮ Spectral spaces of semistar operations

Cites Work

• On strong Mori domains
• Sequence domains and integer-valued polynomials
• Overrings of Prüfer domains
• Pseudo-Integrality
• On w-modules over strong mori domains
• A characterization of cancellation ideals
• Nagata Rings, Kronecker Function Rings, and Related Semistar Operations
• PRÜFER ⋆-MULTIPLICATION DOMAINS AND SEMISTAR OPERATIONS
• On Characterizations of Prüfer Rings.
• A generalization of Kronecker function rings and Nagata rings
• The Cancellation Law for Ideals in a Commutative Ring
• Semistar Invertibility on Integral Domains
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