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Search Results: 1 - 10 of 586143 matches for " P. A. Guil Asensio "
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Flat Model Structures for Nonunital Algebras and Higher K-Theory
S. Estrada,P. A. Guil Asensio
Mathematics , 2009,
Abstract: We prove the existence of a Quillen Flat Model Structure in the category of unbounded complexes of h-unitary modules over a nonunital ring (or a $k$-algebra, with $k$ a field). This model structure provides a natural framework where a Morita-invariant homological algebra for these nonunital rings can be developed. And it is compatible with the usual tensor product of complexes. The Waldhausen category associated to its cofibrations allows to develop a Morita invariant excisive higher $K$-theory for nonunital algebras.
Model category structures arising from Drinfeld vector bundles
S. Estrada,P. A. Guil Asensio,M. Prest,J. Trlifaj
Mathematics , 2009,
Abstract: We present a general construction of model category structures on the category $\mathbb{C}(\mathfrak{Qco}(X))$ of unbounded chain complexes of quasi-coherent sheaves on a semi-separated scheme $X$. The construction is based on making compatible the filtrations of individual modules of sections at open affine subsets of $X$. It does not require closure under direct limits as previous methods. We apply it to describe the derived category $\mathbb D (\mathfrak{Qco}(X))$ via various model structures on $\mathbb{C}(\mathgrak{Qco}(X))$. As particular instances, we recover recent results on the flat model structure for quasi-coherent sheaves. Our approach also includes the case of (infinite-dimensional) vector bundles, and of restricted flat Mittag-Leffler quasi-coherent sheaves, as introduced by Drinfeld. Finally, we prove that the unrestricted case does not induce a model category structure as above in general.
A Quillen Model Structure Approach to the Finitistic Dimension Conjectures
S. Estrada,P. A. Guil Asensio,M. Cortes Izurdiaga
Mathematics , 2009,
Abstract: We explore the interlacing between model category structures attained to classes of modules of finite $\mathcal{X}$-dimension, for certain classes of modules $\mathcal{X}$. As an application we give a model structure approach to the Finitistic Dimension Conjectures and present a new conceptual framework in which these conjectures can be studied.
On the Goldie Dimension of Hereditary Rings and Modules
H. Q. Dinh,P. A. Guil Asensio,S. R. Lopez-Permouth
Mathematics , 2005,
Abstract: We find a bound for the Goldie dimension of hereditary modules in terms of the cardinality of the generator sets of its quasi-injective hull. Several consequences are deduced. In particular, it is shown that every right hereditary module with countably generated quasi-injective hull is noetherian. Or that every right hereditary ring with finitely generated injective hull is artinian, thus answering a long standing open question posed by Dung, Gomez Pardo and Wisbauer.
Automorphism-invariant modules satisfy the exchange property
Pedro A Guil Asensio,Ashish K. Srivastava
Mathematics , 2013,
Abstract: Warfield proved that every injective module has the exchange property. This was generalized by Fuchs who showed that quasi-injective modules satisfy the exchange property. We extend this further and prove that a module invariant under automorphisms of its injective hull satisfies the exchange property. We also show that automorphism-invariant modules are clean and that directly-finite automorphism-invariant modules satisfy the internal cancellation and hence the cancellation property.
Additive Unit Representations in Endomorphism Rings and an Extension of a result of Dickson and Fuller
Pedro A. Guil Asensio,Ashish K. Srivastava
Mathematics , 2013,
Abstract: A module is called automorphism-invariant if it is invariant under any automorphism of its injective hull. Dickson and Fuller have shown that if $R$ is a finite-dimensional algebra over a field $\mathbb F$ with more than two elements then an indecomposable automorphism-invariant right $R$-module must be quasi-injective. In this note, we extend and simplify the proof of this result by showing that any automorphism-invariant module over an algebra over a field with more than two elements is quasi-injective. Our proof is based on the study of the additive unit structure of endomorphism rings.
Automorphism-invariant modules
Pedro A. Guil Asensio,Ashish K. Srivastava
Mathematics , 2014,
Abstract: A module is called automorphism-invariant if it is invariant under any automorphism of its injective envelope. In this survey article we present the current state of art dealing with such class of modules.
Descent of restricted flat Mittag-Leffler modules and generalized vector bundles
Sergio Estrada,Pedro A. Guil Asensio,Jan Trlifaj
Mathematics , 2011,
Abstract: A basic question for any property of quasi--coherent sheaves on a scheme $X$ is whether the property is local, that is, it can be defined using any open affine covering of $X$. Locality follows from the descent of the corresponding module property: for (infinite dimensional) vector bundles and Drinfeld vector bundles, it was proved by Kaplansky's technique of d\'evissage already in \cite[II.\S3]{RG}. Since vector bundles coincide with $\aleph_0$-restricted Drinfeld vector bundles, a question arose in \cite{EGPT} of whether locality holds for $\kappa$-restricted Drinfeld vector bundles for each infinite cardinal $\kappa$. We give a positive answer here by replacing the d\' evissage with its recent refinement involving $\mathcal C$-filtrations and the Hill Lemma.
A note on the construction of finitely injective modules
Pedro A. Guil Asensio,Manuel C. Izurdiaga,Blas Torrecillas
Mathematics , 2012,
Abstract: We develop a technique to construct finitely injective modules which are non trivial, in the sense that they are not direct sums of injective modules. As a consequence, we prove that a ring $R$ is left noetherian if and only if each finitely injective left $R$-module is trivial, thus answering an open question posed by Salce.
New Characterizations of pseudo-Frobenius rings and a generalization of the FGF conjecture
Pedro A. Guil Asensio,Serap Sahinkaya,Ashish K. Srivastava
Mathematics , 2015,
Abstract: We provide new characterizations of pseudo-Frobenius and quasi-Frobenius rings in terms of tight modules. In the process, we also provide fresh perspectives on FGF and CF conjectures. In particular, we propose new natural extensions of these conjectures which connect them with the classical theory of PF rings. Our techniques are mainly based on set-theoretic counting arguments initiated by Osofsky. Several corollaries and examples to illustrate their applications are given.
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