Projective module
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Derived Categories Open
This is the fourth (and last) prepublication version of a book on derived
categories, that will be published by Cambridge University Press. The purpose of the book is to provide solid foundations for the theory of
derived categories, and t…
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Super Finitely Presented Modules and Gorenstein Projective Modules Open
Let $R$ be a commutative ring. An $R$-module $M$ is said to be super finitely\npresented if there is an exact sequence of $R$-modules $\\cdots\\rightarrow\nP_n\\rightarrow\\cdots \\rightarrow P_1\\rightarrow P_0\\rightarrow M\\rightarrow 0…
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Good tilting modules and recollements of derived module categories, II Open
Homological tilting modules of finite projective dimension are investigated. They generalize both classical and good tilting modules of projective dimension at most one, and produce recollements of derived module categories of rings in whi…
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Homological dimension based on a class of Gorenstein flat modules Open
In this paper, we study the relative homological dimension based on the class of projectively coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and Stovicek in [26]. The resulting PGF-dimension of modules has…
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Gendo-symmetric algebras, dominant dimensions and Gorenstein homological algebra Open
We prove that a finite dimensional algebra $A$ with representation-finite subcategory consisting of modules that are semi-Gorenstein-projective and $n$-th syzygy modules is left weakly Gorenstein. This generalises a theorem of Ringel and Z…
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Rank-two Milnor idempotents for the multipullback quantum complex projective plane Open
The $K_0$-group of the C*-algebra of multipullback quantum complex projective plane is known to be $\mathbb{Z}^3$, with one generator given by the C*-algebra itself, one given by the section module of the noncommutative (dual) tautological…
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Gorenstein projective bimodules via monomorphism categories and filtration categories Open
We generalize the monomorphism category from quiver (with monomial relations) to arbitrary finite dimensional algebras by a homological definition. Given two finite dimension algebras $A$ and $B$, we use the special monomorphism category M…
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The Decomposition of a Finitely Generated Module over Some Special Ring Open
This research aims to give the decompositions of a finitely generated module over some special ring, such as the principal ideal domain and Dedekind domain. One of the main problems with module theory is to analyze the objects of the modul…
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A description of Gorenstein projective modules over the tensor products of algebras Open
Let $A$ be a coherent algebra and $B$ be a finite-dimensional Gorenstein algebra over a field $k$. We describe finitely presented Gorenstein projective $A\otimes_k B$-modules in terms of their underlying onesided modules. Moreover, if the …
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Dominant dimension and tilting modules Open
We study which algebras have tilting modules that are both generated and cogenerated by projective-injective modules. Crawley-Boevey and Sauter have shown that Auslander algebras have such tilting modules; and for algebras of global dimens…
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Max-projective modules Open
Weakening the notion of [Formula: see text]-projectivity, a right [Formula: see text]-module [Formula: see text] is called max-projective provided that each homomorphism [Formula: see text], where [Formula: see text] is any maximal right i…
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Wide subcategories of finitely generated Λ-modules Open
We explore some properties of wide subcategories of the category [Formula: see text] of finitely generated left [Formula: see text]-modules, for some artin algebra [Formula: see text] In particular we look at wide finitely generated subcat…
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A HOMOLOGICAL CHARACTERIZATION OF KRULL DOMAINS Open
In this article, we introduce a new type of projective modules, called the weak w-projective module. By using this type of modules, we give a homological characterization of Krull domains. More pre...
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On modules over groups Open
For a finite group G, by the endomorphism ring of a module M over a commutative ring R, we define a structure for M to make it an RG-module so that we study the relations between the properties of R-modules and RG-modules. Mainly, we prove…
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On commutative differential graded algebras Open
In this paper we undertake a basic study on connective commutative differential graded algebras (CDGA), more precisely, piecewise Noetherian CDGA, which is a DG-counter part of commutative Noetherian algebra. We establish basic results for…
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Model structures and relative Gorenstein flat modules Open
We obtain the Gorenstein flat model structure on the category
$\mathsf{Mod}(R)$ of left $R$-modules provided $R$ is a GF-closed ring. Our
approach does not rely on the coherence of the ring and so it is necessarily
different from the same …
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Chern classes in precobordism theories Open
We construct Chern classes of vector bundles in the universal precobordism theory of Annala–Yokura over an arbitrary Noetherian base ring of finite Krull dimension. As an immediate corollary, we show that the Grothendieck ring of vector bu…
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On totally projective <i>QTAG</i>-modules Open
A module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules. In this paper we investigate the class of QTAG-modules whose every …
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On Ding injective, Ding projective and Ding flat modules and complexes Open
We characterize Ding modules and complexes over Ding-Chen rings. We show that over a Ding-Chen ring R, the Ding projective (resp. Ding injective, resp. Ding flat) R-modules coincide with the Gorenstein projective (resp. Gorenstein injectiv…
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Direct limits of Gorenstein injective modules Open
One of the open problems in Gorenstein homological algebra is: when is the class of Gorenstein injective modules closed under arbitrary direct limits? It is known that if the class of Gorenstein injective modules, $\mathcal{GI}$, is closed…
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Structure theory for a class of grade 3 homogeneous ideals defining type 2 compressed rings Open
Let R=k[x,y,z] be a standard graded 3-variable polynomial ring, where k denotes any field. We study grade 3 homogeneous ideals I⊆R defining compressed rings with socle k(−s)⊕k(−2s+1), where s≥3 is some integer. We prove that all such ideal…
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UJ -endomorphism rings Open
In this paper, we introduce and study U J-modules, that is modules M for which their endomorphism rings EM are right U J. We show, in particular, that: (1) if M is a left U J-module over a ring R, then M is Dedekind finite;(2) M is a U J-m…
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Noncommutative G-semihereditary rings Open
In this paper, we introduce and study left (right) [Formula: see text]-semihereditary rings over any associative ring, and these rings are exactly [Formula: see text]-semihereditary rings defined by Mahdou and Tamekkante provided that [For…
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Module traces and Hopf group-coalgebras Open
Let H be a finite-dimensional pivotal and unimodular Hopf algebra over a field k. It was shown in [BBGa] that the projective tensor ideal in H-mod admits a unique non-degenerate modified trace, a natural generalisation of the categorical t…
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Noncommutative Borsuk–Ulam-type conjectures revisited Open
Let H be the C*-algebra of a non-trivial compact quantum group acting freely on a unital C*-algebra A . It was recently conjectured that there does not exist an equivariant *-homomorphism from A (type-I case) or H (type-II case) to the equ…
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On M-injective and M-projective Modules Open
In this study, the concept of m-projective modules is introduced. A right R-module M is said to be m-projective if Ext(M,N)=0 for any m-injective right R-module N. We prove that every right R-module has a special m-projective precover and …
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THE STRUCTURE OF BALANCED BIG COHEN–MACAULAY MODULES OVER COHEN–MACAULAY RINGS Open
Over a Cohen–Macaulay (CM) local ring, we characterize those modules that can be obtained as a direct limit of finitely generated maximal CM modules. We point out two consequences of this characterization: (1) Every balanced big CM module,…
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Finite-direct-injective modules Open
In this paper, we generalize the concept of direct-injective modulesto finite-direct-injective modules. Various basic properties of these modules arestudied. We show that the class of finite-direct-injective modules lies betweenthe class o…
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On a new variation of injective modules Open
In this paper, we provide various properties of GE and GEE-modules, a new variation of injective modules. We call M a GE-module if it has a g-supplement in every extension N and, we call also M a GEE-module if it has ample g-supplements in…
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Co-retractable Modules and Semi-Simplicity Property Open
Co-retractable modules appeared in 2006 by Clark, Lomp and Vanaja. In this article, we present and study the relationships between two known concepts namely semi-simple modules and Co-retractable module. Our concern in this article is to d…