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Matrices over upper triangular bimodules and Δ-filtered modules over quasi-hereditary algebras

Thomas Brüstle, Lutz Hille (2000)

Colloquium Mathematicae

Let Λ be a directed finite-dimensional algebra over a field k, and let B be an upper triangular bimodule over Λ. Then we show that the category of B-matrices mat B admits a projective generator P whose endomorphism algebra End P is quasi-hereditary. If A denotes the opposite algebra of End P, then the functor Hom(P,-) induces an equivalence between mat B and the category ℱ(Δ) of Δ-filtered A-modules. Moreover, any quasi-hereditary algebra whose category of Δ-filtered modules is equivalent to mat...

Matrix rings with summand intersection property

F. Karabacak, Adnan Tercan (2003)

Czechoslovak Mathematical Journal

A ring R has right SIP (SSP) if the intersection (sum) of two direct summands of R is also a direct summand. We show that the right SIP (SSP) is the Morita invariant property. We also prove that the trivial extension of R by M has SIP if and only if R has SIP and ( 1 - e ) M e = 0 for every idempotent e in R . Moreover, we give necessary and sufficient conditions for the generalized upper triangular matrix rings to have SIP.

Minimal prime ideals of skew polynomial rings and near pseudo-valuation rings

Vijay Kumar Bhat (2013)

Czechoslovak Mathematical Journal

Let R be a ring. We recall that R is called a near pseudo-valuation ring if every minimal prime ideal of R is strongly prime. Let now σ be an automorphism of R and δ a σ -derivation of R . Then R is said to be an almost δ -divided ring if every minimal prime ideal of R is δ -divided. Let R be a Noetherian ring which is also an algebra over ℚ ( ℚ is the field of rational numbers). Let σ be an automorphism of R such that R is a σ ( * ) -ring and δ a σ -derivation of R such that σ ( δ ( a ) ) = δ ( σ ( a ) ) for all a ∈ R . Further, if for any...

Modules.

Cockett, J. R. B., Koslowski, J., Seely, R. A. G., Wood, R. J. (2003)

Theory and Applications of Categories [electronic only]

Modules commuting (via Hom) with some colimits

Robert El Bashir, Tomáš Kepka, Petr Němec (2003)

Czechoslovak Mathematical Journal

For every module M we have a natural monomorphism Ψ : ∐ i ∈ I H o m R ( M , A i ) → H o m R M , ∐ i ∈ I A i and we focus our attention on the case when Ψ is also an epimorphism. Some other colimits are also considered.

Modules commuting (via Hom) with some limits

Robert El Bashir, Tomáš Kepka (1998)

Fundamenta Mathematicae

For every module M we have a natural monomorphism   Φ : ∐ i ∈ I H o m R ( A i , M ) → H o m R ( ∏ i ∈ I A i , M ) and we focus attention on the case when Φ is also an epimorphism. The corresponding modules M depend on thickness of the cardinal number card(I). Some other limits are also considered.

Modules continus

Jacques Bichot (1971)

Publications du Département de mathématiques (Lyon)

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