A Connection Between Weak Regularity and the Simplicity of Prime Factor Rings

DOI10.2307/2160840zbMath0814.16001OpenAlexW4252979368MaRDI QIDQ4311370

Jin Yong Kim, Gary F. Birkenmeier, Jae Keol Park

Publication date: 13 June 1995

Full work available at URL: https://doi.org/10.2307/2160840

zbMATH Keywords

reduced ringweakly regular

Mathematics Subject Classification ID

Prime and semiprime associative rings (16N60) Infinite-dimensional simple rings (except as in 16Kxx) (16D30) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (23)

Unnamed Item ⋮ Weakly regular rings with ACC on annihilators and maximality of strongly prime ideals of weakly regular rings. ⋮ Structure of insertion property by powers ⋮ Weakly regular rings ⋮ On subdirect products of division rings ⋮ Symmetric ring property on nil ideals ⋮ A note on weak regularity in general rings. ⋮ On semiabelian \(\pi\)-regular rings. ⋮ On the structures of Abelian \(\pi\)-regular rings. ⋮ Examples of strongly \(\pi\)-regular rings. ⋮ On a property of polynomial rings over reversible rings ⋮ Unnamed Item ⋮ Additive decomposition of ideals ⋮ Rings whose nilpotents form a multiplicative set ⋮ Regularity conditions and the simplicity of prime factor rings ⋮ Veldsman's classes of associative rings ⋮ Homomorphisms close to regular and their applications. ⋮ A characterization of minimal prime ideals ⋮ ON NI AND QUASI-NI RINGS ⋮ ABELIAN PROPERTY CONCERNING FACTORIZATION MODULO RADICALS ⋮ Soclean rings ⋮ On rings whose prime ideals are completely prime ⋮ On reduced rings with prime factors simple

Cites Work

• On the von Neumann regularity of rings with regular prime factor rings
• On two analogues of Cohen's theorem
• Epimorphismen von kommutativen Ringen
• Commutative rings with restricted minimum condition
• Reflexive ideals
• Prime Ideals and Sheaf Representation of a Pseudo Symmetric Ring
• On Functional Representations of a Ring without Nilpotent Elements
• On the Representation of Modules by Sheaves of Factor Modules
• Weakly Regular Rings
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