Regularly biserial algebras
Regularly weakly based modules over right perfect rings and Dedekind domains
A weak basis of a module is a generating set of the module minimal with respect to inclusion. A module is said to be regularly weakly based provided that each of its generating sets contains a weak basis. We study (1) rings over which all modules are regularly weakly based, refining results of Nashier and Nichols, and (2) regularly weakly based modules over Dedekind domains.
Rein inseparable Körpererweiterungen.
Relationship of certain rings of infinite matrices over integers
Sia l'insieme degli interi non negativi e l'anello degli interi. Sia l'anello delle matrici su che hanno solo un numero finito di cifre non nulle in ogni linea ed in ogni colonna. Sia il sottoanello generato da e , dove (rispettivamente ) è ottenuto dalla matrice identità muovendo gli 1 una posizione a destra (rispettivamente in giù). Sia pure il sottoanello di generato da e . Infine sia il sottoanello delle matrici di che hanno solo un numero finito di cifre non nulle....
Relative Auslander bijection in -exangulated categories
The aim of this article is to study the relative Auslander bijection in -exangulated categories. More precisely, we introduce the notion of generalized Auslander-Reiten-Serre duality and exploit a bijection triangle, which involves the generalized Auslander-Reiten-Serre duality and the restricted Auslander bijection relative to the subfunctor. As an application, this result generalizes the work by Zhao in extriangulated categories.
Relative Auslander-Reiten sequences for quasi-hereditary algebras
Let A be a finite-dimensional algebra which is quasi-hereditary with respect to the poset (Λ, ≤), with standard modules Δ(λ) for λ ∈ Λ. Let ℱ(Δ) be the category of A-modules which have filtrations where the quotients are standard modules. We determine some inductive results on the relative Auslander-Reiten quiver of ℱ(Δ).
Relative Brauer groups. III.
Relative Buchsbaumness of bigraded modules
We study finitely generated bigraded Buchsbaum modules over a standard bigraded polynomial ring with respect to one of the irrelevant bigraded ideals. The regularity and the Hilbert function of graded components of local cohomology at the finiteness dimension level are considered.
Relative coherence and preenvelopes.
Relative exact covers
Recently Rim and Teply [11] found a necessary condition for the existence of -torsionfree covers with respect to a given hereditary torsion theory for the category -mod. This condition uses the class of -exact modules; i.e. the -torsionfree modules for which every its -torsionfree homomorphic image is -injective. In this note we shall show that the existence of -torsionfree covers implies the existence of -exact covers, and we shall investigate some sufficient conditions for the converse....
Relative hermitian Morita theory. Part II: Hermitian Morita contexts.
We introduce the notion of a relative hermitian Morita context between torsion triples and we show how these induce equivalences between suitable quotient categories of left and right modules.Due to the lack of involutive bimodules, the induced Morita equivalences are not necessarily hermitian, however.
Relative injectivity and CS-modules.
Relative Invarianten und nicht-assoziative Algebren.
Relative natural classes and relative injectivity.
Relative normalizing extensions.
Relative purity over Noetherian rings
Relative theory in subcategories
We generalize the relative (co)tilting theory of Auslander-Solberg in the category mod Λ of finitely generated left modules over an artin algebra Λ to certain subcategories of mod Λ. We then use the theory (relative (co)tilting theory in subcategories) to generalize one of the main result of Marcos et al. [Comm. Algebra 33 (2005)].
Relative weak derived functors
Let be a ring, a fixed non-negative integer, the class of all left -modules with weak injective dimension at most , and the class of all right -modules with weak flat dimension at most . Using left (right) -resolutions and the left derived functors of Hom we study the weak injective dimensions of modules and rings. Also we prove that is right balanced on by , and investigate the global right -dimension of by right derived functors of .
Relatively coarse sequential convergence
We generalize the notion of a coarse sequential convergence compatible with an algebraic structure to a coarse one in a given class of convergences. In particular, we investigate coarseness in the class of all compatible convergences (with unique limits) the restriction of which to a given subset is fixed. We characterize such convergences and study relative coarseness in connection with extensions and completions of groups and rings. E.g., we show that: (i) each relatively coarse dense group precompletion...
Relatively exact modules
Rim and Teply [10] investigated relatively exact modules in connection with the existence of torsionfree covers. In this note we shall study some properties of the lattice of submodules of a torsionfree module consisting of all submodules of such that is torsionfree and such that every torsionfree homomorphic image of the relative injective hull of is relatively injective. The results obtained are applied to the study of relatively exact covers of torsionfree modules. As an application...