1,721,017 research outputs found
Total C-denseness
Full text linkWe study total C-denseness, for a closure operator C, in a large class of categories. We give necessary and sufficient conditions for total C- denseness to be a denseness with respect to a suitable closure operator. Examples and applications in the categories of abstract modules, abelian groups, topological abelian groups and topological spaces are given
On global controllability of linear time dependent control systems
No full textLet (A,B) be a linear time-dependent control process, defined on an open interval J=]α,ω[ with α≥−∞ and ω≤∞. In this paper we give a description of the function τ:I→J, τ(t)=inf{t′>t:(A,B) is [t,t′]-globally controllable from 0}, where I={t∈J: there exists t′∈J with (A,B)[t,t′]-globally controllable from 0}
On the complementarity of two quasi-tilting triples
No full textAbstract. Let R and S be two rings. Each category equivalence between a
torsion class of left (right) R-modules and a torsion-free class of left (right) S-
modules is represented by a left (right) quasi-tilting triple. Suppose we have a
−→ −→ pair of equivalences T ←− Y and X ←− F, between the torsion class T of R-
modules and the torsion-free class Y of S-modules and between the torsion class X of S-modules and the torsion-free class F of R-modules. Denote by (R, V, S) and (S, U, R) the quasi-tilting triples representing these equivalences. We say that (R,V,S) and (S,U,R) are complementary if (T ,F) and (X,Y) are torsion theories in R-Mod and S-Mod, respectively. We find necessary and sufficient conditions on the bimodules RVS and SUR to have the complementarity of (R,V,S) and (S, U, R)
On a finitistic cotilting-type duality
No full textLet R and S be arbitrary associative rings. Given a bimodule RWS, we denote by ∆? and Γ? the functors Hom?(−,W) and Ext1?(−,W), where ? = R or S. We say that RWS is a finitistic weakly cotilting bimodule (briefly FWC) if for each module M cogenerated by W, finitely generated or homomorphic image of a finite direct sum of copies of W, ΓM = 0 = Ext2(M,W). We are able to describe, on a large class of finitely generated modules, the cotilting- type duality induced by a FWC-bimodule
n-Cotilting and n-Tilting modules over ring extensions
Full text linkWhen Gamma is a ring extension of R, conditions are found to insure that the notion of n-tilting module and n-cotilting module pass from a left R-module V to the induced left Gamma-modules Tor (R)(i)(Gamma, V) and Ext (i)(R) (Gamma, V), 0 <= i <= n
Tilting Modules of Finite Projective Dimension: Sequentially Static and Costatic Modules
No full textIn [5], Miyashita introduced tilting modules of nite projective dimension. A tilting
module AV of projective dimension less or equal than r furnishes r + 1 equivalences
between subcategories of A-Mod and End V -Mod: we call static and costatic the modules
in A-Mod and End V -Mod, respectively, involved in these equivalences. In this paper we
characterize the modules in A-Mod and End V -Mod which have a ltration with static
and costatic factors, respectively
On the classes of dense and closed subobjects
Full text linkWe provide analogous characterizations of the families of dense and of closed subobjects with respect to closure operators. The analogous behavior of hereditary and minimal closure operators with respect to the families of dense and of closed subobjects, respectively, is pointed out. We prove that, in the category of topological abelian groups, the total denseness cannot be described as denseness with respect to a closure operator
Sequentially reflexive modules
No full textWe generalize the homological characterization of sequentially Cohen-Macaulay modules over a graded Gorenstein algebra to sequentially reflexive modules over Noetherian, not necessarily commutative rings, with a N-partial cotilting bimodule playing the role of the graded Gorenstein algebra. In such a way we get a complete version of the "Cotilting Theorem". Finally, conditions are found to insure that the "N-partial cotilting notion" pass through a finite ring extension
ON THE EXISTENCE OF A FINEST EQUIVALENT LINEAR TOPOLOGY
No full textA duality is introduced to prove the existance of a finest linear topology equivalent to a given one for linearly topologized modules. Various properties of this finest topology are obtained
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