Displaying similar documents to “Notes on slender prime rings”

Dually steady rings

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

Acta Universitatis Carolinae. Mathematica et Physica

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⋂ -compact modules

Tomáš Kepka (1995)

Commentationes Mathematicae Universitatis Carolinae

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The duals of ∪ -compact modules are briefly discussed.

On rings close to regular and p -injectivity

Roger Yue Chi Ming (2006)

Commentationes Mathematicae Universitatis Carolinae

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The following results are proved for a ring A : (1) If A is a fully right idempotent ring having a classical left quotient ring Q which is right quasi-duo, then Q is a strongly regular ring; (2) A has a classical left quotient ring Q which is a finite direct sum of division rings iff A is a left TC -ring having a reduced maximal right ideal and satisfying the maximum condition on left annihilators; (3) Let A have the following properties: (a) each maximal left ideal of A is either a two-sided...

On commutative rings whose prime ideals are direct sums of cyclics

M. Behboodi, A. Moradzadeh-Dehkordi (2012)

Archivum Mathematicum

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In this paper we study commutative rings R whose prime ideals are direct sums of cyclic modules. In the case R is a finite direct product of commutative local rings, the structure of such rings is completely described. In particular, it is shown that for a local ring ( R , ℳ ) , the following statements are equivalent: (1) Every prime ideal of R is a direct sum of cyclic R -modules; (2) ℳ = ⨁ λ ∈ Λ R w λ where Λ is an index set and R / Ann ( w λ ) is a principal ideal ring for each λ ∈ Λ ; (3) Every prime ideal of R is a direct...