Displaying similar documents to “Steady ideals and rings”

ω 1 -generated uniserial modules over chain rings

Jan Žemlička (2004)

Commentationes Mathematicae Universitatis Carolinae

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The purpose of this paper is to provide a criterion of an occurrence of uncountably generated uniserial modules over chain rings. As we show it suffices to investigate two extreme cases, nearly simple chain rings, i.e. chain rings containing only three two-sided ideals, and chain rings with “many” two-sided ideals. We prove that there exists an ω 1 -generated uniserial module over every non-artinian nearly simple chain ring and over chain rings containing an uncountable strictly increasing...

Rings with zero intersection property on annihilators: Zip rings.

Carl Faith (1989)

Publicacions Matemàtiques

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Zelmanowitz [12] introduced the concept of ring, which we call right zip rings, with the defining properties below, which are equivalent: (ZIP 1) If the right anihilator X⊥ of a subset X of R is zero, then X1 ⊥ = 0 for a finite subset X1 ⊆ X. (ZIP 2) If L is a left ideal and if L⊥ = 0, then L1 ...

Dually steady rings

Robert El Bashir, Tomáš Kepka, Jan Žemlička (2011)

Acta Universitatis Carolinae. Mathematica et Physica

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Embedding torsionless modules in projectives.

Carl Faith (1990)

Publicacions Matemàtiques

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In this paper we study a condition right FGTF on a ring R, namely when all finitely generated torsionless right R-modules embed in a free module. We show that for a von Neuman regular (VNR) ring R the condition is equivalent to every matrix ring R is a Baer ring; and this is right-left symmetric. Furthermore, for any Utumi VNR, this can be strengthened: R is FGTF iff R is self-injective.