Nil-ideals, \(J\)-ideals and their generalizations in commutative rings

DOI10.1007/s13366-022-00668-6OpenAlexW4304808215MaRDI QIDQ6067057

Abdeslam Mimouni

Publication date: 16 November 2023

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13366-022-00668-6

zbMATH Keywords

pullbacks\(Q\)-ideal\(J\)-idealtrivial extension ringamalgamation ringradically \(J\)-ideal

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Class groups (13C20)

Cites Work

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• Idealization of a module
• A construction of Gorenstein rings
• The amalgamated duplication of a ring along a multiplicative-canonical ideal
• Topologically defined classes of commutative rings
• Commutative coherent rings
• \(D+M\) constructions with general overrings
• Pseudo-valuation domains
• Coherentlike conditions in pullbacks
• On the class group and the local class group of a pullback
• Overrings and divisorial ideals of rings of the form \(D+M\)
• Trivial Extensions Defined by Coherent-like Conditions
• AN AMALGAMATED DUPLICATION OF A RING ALONG AN IDEAL: THE BASIC PROPERTIES
• Amalgamated algebras along an ideal
• CPI-Extensions: Overrings of Integral Domains with Special Prime Spectrums
• Pairs of Rings with the Same Prime Ideals
• Quasi $J$-submodules
• N-ideals of commutative rings

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