Rings described by various purities

DOI10.1080/00927879908826554zbMath0943.16004OpenAlexW2025395763MaRDI QIDQ4241647

Philipp Rothmaler, Gennadi Puninski, M. Y. Prest

Publication date: 19 June 2000

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

Full work available at URL: https://doi.org/10.1080/00927879908826554

zbMATH Keywords

local ringssystems of linear equationslocalizationspuritieselementary dualitypure embeddingsdistributive ringsrelative divisibilitylocal RD-ringsRD-domainsright Warfield rings

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Injective modules, self-injective associative rings (16D50) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Other classes of modules and ideals in associative algebras (16D80) Applications of logic in associative algebras (16B70)

Related Items (24)

Pure injective envelopes of finite length modules over a generalized Weyl algebra ⋮ \textit{RD}-flatness and \textit{RD}-injectivity of simple modules ⋮ Unnamed Item ⋮ Rings whose cyclic modules are pure-injective or pure-projective ⋮ On the structure of pure-projective modules and some applications ⋮ Mittag-Leffler modules ⋮ Rings over which every \(RD\)-projective module is a direct sum of cyclically presented modules. ⋮ On minimal absolutely pure domain of RD-flat modules ⋮ Some model theory of modules over Bézout domains. The width ⋮ On subinjectivity domains of pure-injective modules ⋮ Rings in which every ideal is pure-projective or FP-projective ⋮ On FC-Purity and I-Purity of Modules and Köthe Rings ⋮ Cantor-Bendixson Rank of the Ziegler Spectrum Over a Commutative Valuation Domain ⋮ Pure-projective modules and positive constructibility ⋮ Some new dimensions of modules and rings ⋮ Comparison of Some Purities, Flatnesses and Injectivities ⋮ Torsion-free, Divisible, and Mittag-Leffler Modules ⋮ PURITY RELATIVE TO CLASSES OF FINITELY PRESENTED MODULES ⋮ RD-Flatness and RD-Injectivity ⋮ Finite length and pure-injective modules over a ring of differential operators ⋮ C-Pure Projective Modules ⋮ ∑–pure—injective modules over a commutative prüfer ring ⋮ Rd-phantom and RD-Ext-phantom morphisms ⋮ On subinjectivity domains of RD-injective modules

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