51 research outputs found
On classes defining a homological dimension
A class of objects of an abelian category is said
to define a \emph{homological dimension} if for any object in the
length of any -resolution is uniquely determined. In the present
paper we investigate classes satisfying this property.Comment: to appear in Contribution to Module Theory, de Gruyter 200
Derived dualities induced by a 1-cotilting bimodule
In this paper we characterize the modules and the complexes involved in the
dualities induced by a 1-cotilting bimodule in terms of a linear compactness
condition. Our result generalizes the classical characterization of reflexive
modules with respect to Morita dualities. The linear compactness notion
considered, permits us to obtain finiteness properties of the rings and modules
involved
Reflexivity in Derived Categories
An adjoint pair of contravariant functors between abelian categories can be
extended to the adjoint pair of their derived functors in the associated
derived categories. We describe the reflexive complexes and interpret the
achieved results in terms of objects of the initial abelian categories. In
particular we prove that, for functors of any finite cohomological dimension,
the objects of the initial abelian categories which are reflexive as stalk
complexes form the largest class where a Cotilting Theorem in the sense of
Colby and Fuller works
Pr\ufcfer modules over Leavitt path algebras
Let LK(E) denote the Leavitt path algebra associated to the finite graph E and field K. For any closed path c
in E, we define and investigate the uniserial, artinian, non-Noetherian left LK(E)-module U_{E,c 121}. The unique simple factor of each proper submodule of U_{E,c 121}is isomorphic to the Chen simple module V_[c 1e]. In our main result, we classify those closed paths c for which U_{E,c 121}
is injective. In this situation, U_{E,c 121} is the injective hull of V_[c 1e]
Pr\"ufer modules over Leavitt path algebras
Let denote the Leavitt path algebra associated to the finite graph
and field . For any closed path in , we define and investigate
the uniserial, artinian, non-noetherian left -module . The
unique simple factor of each proper submodule of is isomorphic to
the Chen simple module . In our main result, we classify those
closed paths for which is injective. In this situation,
is the injective hull of .Comment: 24 pages. Submitted for publication July 2017. Comments are welcome
Extensions of simple modules over Leavitt path algebras
Let be a directed graph, any field, and let denote the
Leavitt path algebra of with coefficients in . For each rational
infinite path of we explicitly construct a projective resolution
of the corresponding Chen simple left -module .
Further, when is row-finite, for each irrational infinite path of
we explicitly construct a projective resolution of the corresponding Chen
simple left -module . For Chen simple modules we
describe by presenting an explicit -basis. For
any graph containing at least one cycle, this description guarantees the
existence of indecomposable left -modules of any prescribed finite
length.Comment: updated: dedication to Alberto Facchini on the occasion of his 60th
Birthday added in front matte
Injective modules over the Jacobson algebra
For a field , let denote the Jacobson algebra . We give an explicit construction of the injective envelope
of each of the (infinitely many) simple left -modules.
Consequently, we obtain an explicit description of a minimal injective
cogenerator for . Our approach involves realizing up
to isomorphism as the Leavitt path -algebra of an appropriate graph
, which thereby allows us to utilize important machinery developed
for that class of algebras.Comment: 16 page
EARLY IMPACT PROCEDURES FOR FLOOD EVENTSFEBRUARY 2007 MOZAMBIQUE FLOOD
Satellite images and GIS procedures are key elements for emergency management, especially in case of events hitting developing countries, more vulnerable to calamities and less prepared to face them. This article aims to show the procedure applied for the pro-duction of a cartography of flooded areas during the early impact phase; these activities are developed within ITHACA, centre of excellence, in charge of giving technological support to the WFP (World Food Programme), the biggest agency of the UN. The flood in
Mozambique, occurred in January 2007, is illustrated as an example of events management
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