A note on existence of envelopes and covers

DOI10.1017/S0004972700021791zbMath0882.16002OpenAlexW2056796078MaRDI QIDQ4346918

Nan Qing Ding, Jian-Long Chen

Publication date: 2 March 1998

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972700021791

zbMATH Keywords

epimorphismsautomorphismshomomorphismsdirect productsdirect summandsprojective coversenvelopesinjective right modulesfinitely presented modulesflat envelopesfinitely generated submodulespre-envelopesfinitely generated free modulesflat right modulesclasses of right modules

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Free, projective, and flat modules and ideals in associative algebras (16D40) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Automorphisms and endomorphisms (16W20)

Related Items (24)

RELATIVE COHERENCE OF RINGS ⋮ When Does Every Simple Module Have a Projective Envelope? ⋮ Weak Injective and Weak Flat Modules ⋮ Relatively Endocoherent Modules ⋮ FI-injective and FI-flat modules. ⋮ Relative extensions of modules and homology groups ⋮ Unnamed Item ⋮ Strongly $(\mathcal{T},n)$-coherent rings, $(\mathcal{T},n)$-semihereditary rings and $(\mathcal{T},n)$-regular rings ⋮ Finitely projective modules with respect to a semidualizing module ⋮ Category of n -weak injective and n -weak flat modules with respect to special super presented modules ⋮ On envelopes and covers in the category of short exact sequences ⋮ \(I\)-\(n\)-coherent rings, \(I\)-\(n\)-semihereditary rings, and \(I\)-regular rings. ⋮ New characterizations of pseudo-coherent rings ⋮ Weak Global Dimension of Coherent Rings ⋮ Relative coherent modules and semihereditary modules ⋮ Phantom envelopes and Ext-phantom covers of modules ⋮ J-COHERENT RINGS ⋮ Coherent rings and absolutely pure precovers ⋮ Relative Projective Modules and Relative Injective Modules ⋮ Normal families: New perspectives ⋮ On subprojectivity domains of g-semiartinian modules ⋮ Envelopes and Covers by Modules of FiniteFP-Injective and Flat Dimensions ⋮ On rings with envelopes and covers regarding to C3, D3 and flat modules ⋮ \(M\)-\(\mathcal A\)-injective (flat) and strongly \(\mathcal B\)-injective (flat) modules.

Cites Work

• Embedding torsionless modules in projectives
• Resolvents and dimensions of modules and rings
• Coherence for polynomial rings
• Finite splitness and finite projectivity
• Flat envelopes in commutative rings
• Injective and flat covers, envelopes and resolvents
• Pure submodules of direct products of free modules
• The flat dimensions of injective modules
• On flat and projective envelopes
• Relative coherence and preenvelopes
• Semiregular Modules and Rings
• Relative injective covers
• Absolutely Pure Modules
• Absolutely Pure Modules
• Flat and FP-Injectivity

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