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Displaying 201 – 220 of 1161

Differentiation and splitting for lattices over orders

Wolfgang Rump (2001)

Colloquium Mathematicae

We extend our module-theoretic approach to Zavadskiĭ’s differentiation techniques in representation theory. Let R be a complete discrete valuation domain with quotient field K, and Λ an R-order in a finite-dimensional K-algebra. For a hereditary monomorphism u: P ↪ I of Λ-lattices we have an equivalence of quotient categories $\partial ̃_{u} : Λ - l a t / [ℋ] ⭇ δ_{u} Λ - l a t / [B]$ which generalizes Zavadskiĭ’s algorithms for posets and tiled orders, and Simson’s reduction algorithm for vector space categories. In this article we replace u by a more...

Ding projective and Ding injective modules over trivial ring extensions

Lixin Mao (2023)

Czechoslovak Mathematical Journal

Let $R ⋉ M$ be a trivial extension of a ring $R$ by an $R$ - $R$ -bimodule $M$ such that $M_{R}$ , $_{R} M$ , ${(R, 0)}_{R ⋉ M}$ and $_{R ⋉ M} (R, 0)$ have finite flat dimensions. We prove that $(X, α)$ is a Ding projective left $R ⋉ M$ -module if and only if the sequence $M \otimes_{R} M \otimes_{R} X \overset{M \otimes α}{⟶} M \otimes_{R} X \overset{α}{\to} X$ is exact and $coker (α)$ is a Ding projective left $R$ -module. Analogously, we explicitly describe Ding injective $R ⋉ M$ -modules. As applications, we characterize Ding projective and Ding injective modules over Morita context rings with zero bimodule homomorphisms.

Direct products of linearly compact primary rings

P. N. Anh (1986)

Rendiconti del Seminario Matematico della Università di Padova

Direct sums of $J$ -rings and radical rings.

Guo, Xiuzhan (1995)

International Journal of Mathematics and Mathematical Sciences

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.