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Direct sums of semi-projective modules

Derya Keskin Tütüncü, Berke Kaleboğaz, Patrick F. Smith (2012)

Colloquium Mathematicae

We investigate when the direct sum of semi-projective modules is semi-projective. It is proved that if R is a right Ore domain with right quotient division ring Q ≠ R and X is a free right R-module then the right R-module Q ⊕ X is semi-projective if and only if there does not exist an R-epimorphism from X to Q.

Directing components for quasitilted algebras

Flávio Coelho (1999)

Colloquium Mathematicae

We show here that a directing component of the Auslander-Reiten quiver of a quasitilted algebra is either postprojective or preinjective or a connecting component.

Distributive lattices of t-k-Archimedean semirings

Tapas Kumar Mondal (2011)

Discussiones Mathematicae - General Algebra and Applications

A semiring S in 𝕊𝕃⁺ is a t-k-Archimedean semiring if for all a,b ∈ S, b ∈ √(Sa) ∩ √(aS). Here we introduce the t-k-Archimedean semirings and characterize the semirings which are distributive lattice (chain) of t-k-Archimedean semirings. A semiring S is a distributive lattice of t-k-Archimedean semirings if and only if √B is a k-ideal, and S is a chain of t-k-Archimedean semirings if and only if √B is a completely prime k-ideal, for every k-bi-ideal B of S.

Dually steady rings

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

Acta Universitatis Carolinae. Mathematica et Physica

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