A Counter Example to a Conjecture of Johns

DOI10.2307/2159289zbMath0762.16011OpenAlexW4241777678MaRDI QIDQ4022079

Pere Menal, Carl Faith

Publication date: 17 January 1993

Full work available at URL: https://doi.org/10.2307/2159289

zbMATH Keywords

right Noetherian ringright annihilatorfinite left Goldie dimensionexistentially closed skew fieldright Artiniansplit null extensionright Johns ringright Noetherian domainsimple right \(A\)-module

Mathematics Subject Classification ID

Injective modules, self-injective associative rings (16D50) Infinite-dimensional and general division rings (16K40) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Noetherian rings and modules (associative rings and algebras) (16P40)

Related Items

Unnamed Item ⋮ Rings in which certain right ideals are direct summands of annihilators ⋮ Unnamed Item ⋮ On Noetherian rings with essential socle ⋮ Comultiplication modules over commutative rings ⋮ The Structure of Johns Rings ⋮ A New Duality Theorem for Semisimple Modules and Characterization of Villamayor Rings ⋮ Annihilators and the CS-condition ⋮ Johns modules and quasi-Johns modules

Cites Work

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• Annihilator conditions in Noetherian rings
• Rings whose cyclic modules have finitely generated socle
• On twisted polynomial rings
• Finitely embedded modules over Noetherian rings
• Division Rings and V-Domains
• Rings satisfying certain chain conditions.
• Homological properties of the ring of differential polynomials