SMALL AND LARGE IDEALS OF AN ASSOCIATIVE RING

DOI10.1142/S021949881350151XzbMath1298.16002OpenAlexW2108513896MaRDI QIDQ5420502

Greg G. Oman

Publication date: 13 June 2014

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s021949881350151x

zbMATH Keywords

cofinalitiescardinalitiesArtinian ringsNoetherian ringsdivision ringsascending chain conditiongeneralized continuum hypothesisdiscrete valuation ringssmall idealslarge ideals

Mathematics Subject Classification ID

Ideals and multiplicative ideal theory in commutative rings (13A15) Ideals in associative algebras (16D25) Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) (16P70)

Related Items (8)

Residually small commutative rings ⋮ Residual smallness in commutative algebra ⋮ Countably coverable rings ⋮ Unital rings with cardinality restrictions on unital subrings ⋮ An infinite cardinal-valued Krull dimension for rings ⋮ Unnamed Item ⋮ A characterization of large Dedekind domains ⋮ On the existence of maximal subrings in commutative noetherian rings

Cites Work

• Unnamed Item
• Jónsson posets and unary Jónsson algebras
• Idealization of a module
• A prime ideal principle in commutative algebra
• Jónsson \(\omega _ 0\)-generated algebraic field extensions
• On Jónsson algebras over a commutative ring
• On Modules Whose Proper Homomorphic Images Are of Smaller Cardinality
• Jónsson Modules over Noetherian Rings
• Cardinalities of Residue Fields of Noetherian Integral Domains
• An Application of Jonsson Modules to Some Questions Concerning Proper Subrings.
• Residually Finite Rings
• Rings with Finite Norm Property

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