On rings with restricted minimum condition

DOI10.1007/BF01194021zbMath0657.16007MaRDI QIDQ1110632

Dinh Van Huynh, Phan Dan

Publication date: 1988

Published in: Archiv der Mathematik (Search for Journal in Brave)

zbMATH Keywords

direct sumuniform right idealsright noetherianartinian moduleartinian idealrestricted minimum conditionright hereditary right CPA rings

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Chain conditions on annihilators and summands: Goldie-type conditions (16P60) Artinian rings and modules (associative rings and algebras) (16P20) Noetherian rings and modules (associative rings and algebras) (16P40)

Related Items

Conditions for a ring to be Noetherian or Artinian, Relatively extending modules., On automorphism-invariant rings with chain conditions, Rings over which every \(RD\)-projective module is a direct sum of cyclically presented modules., Some results on V-rings and weakly V-rings., On the restricted minimum condition for rings, On some classes of Artinian rings, On serial Noetherian rings, On modules with finite uniform and Krull dimension, Restricted minimum condition in reduced commutative rings, Projectivity relative to closed (neat) submodules, Rings with many direct summands

Cites Work

• Unnamed Item
• Unnamed Item
• Modules locally of serial type
• Baer rings and quasi-continuous rings have a MDSN
• On extending property on direct sums of uniform modules
• On a Warfield's theorem on hereditary rings
• Rings all of whose finitely generated modules are injective
• Ideals and modules of simple Noetherian hereditary rings
• On rings whose simple modules are injective
• Semi-Prime Rings with Maximum Condition
• A characterization of artinian rings
• A Right PCI Ring is Right Noetherian
• RINGS IN WHICH EVERY COMPLEMENT RIGHT IDEAL IS A DIRECT SUMMAND
• π-injective modules and rings whose cyclics are π-injective
• Rings Characterized by their Cyclic Modules
• Nonsingular Rings
• Singular torsion and the splitting properties