Differentially trivial left Noetherian rings
We characterize left Noetherian rings which have only trivial derivations.
Differentiation and splitting for lattices over orders
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 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
Let be a trivial extension of a ring by an --bimodule such that , , and have finite flat dimensions. We prove that is a Ding projective left -module if and only if the sequence is exact and is a Ding projective left -module. Analogously, we explicitly describe Ding injective -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
Direct sums of -rings and radical rings.
Direct sums of semi-projective modules
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
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
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.
Divisible and Codivisible Modules.
Dominant Dimension of Double Centralizers.
Double Centralizers and Dominant Dimensions.
Dreiecks-Darstellung von Endomorphismenringen injektiver Moduln.
Dual modules and reflexive modules with respect to a semidualizing module
Let be a semidualizing module over a commutative ring. We first investigate the properties of -dual, -torsionless and -reflexive modules. Then we characterize some rings such as coherent rings, -coherent rings and FP-injectivity of using -dual, -torsionless and -reflexive properties of some special modules.
Dualità sul completamento naturale di un anello noetheriano
Dualities over compact rings
Duality and Completions of Linearly Topologized Modules.
Duality over Auslander-Gorenstein rings.
Duality properties of injective modules
Duality Theorem of Character Modules for Rings with Minimum Condition.
Dually slender modules and steady rings.