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Krull-Schmidt categories and projective covers [PDF]
Expositiones Mathematicae, 2014 Krull-Schmidt categories are additive categories such that each object decomposes into a finite direct sum of indecomposable objects having local endomorphism rings.
Atiyah +9 more
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Projective covers and minimal free resolutions [PDF]
International Journal of Mathematics and Mathematical Sciences, 1996 Using a generalization of the definition of the projective cover of a module, a special type of surjective free resolution, known as the projective cover of a complex, may be defined.
Mark A. Goddard
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Projective Covers of Flat Contramodules [PDF]
International Mathematics Research Notices, 2021 Abstract We show that a direct limit of projective contramodules (over a right linear topological ring) is projective if it has a projective cover. A similar result is obtained for $\infty $-strictly flat contramodules of projective dimension not exceeding $1$, using an argument based on the notion of the topological Jacobson radical ...
Bazzoni, S. +2 more
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An atlas of K3 surfaces with finite automorphism group [PDF]
Épijournal de Géométrie Algébrique, 2022 We study the geometry of the K3 surfaces $X$ with a finite number automorphisms and Picard number $\geq 3$. We describe these surfaces classified by Nikulin and Vinberg as double covers of simpler surfaces or embedded in a projective space.
Xavier Roulleau
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Vanishing Property of BRST Cohomology for Modified Highest Weight Modules
Axioms, 2023 We construct certain modified highest weight modules which are called quasi highest weight modules in this paper. Using the quasi highest weight modules, we introduce a new category of modules over an affine Lie superalgebra which contains projective ...
Namhee Kwon
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Projective Covering Designs [PDF]
Bulletin of the London Mathematical Society, 1993 A \((2,k,v)\) covering design is a pair \((X,{\mathcal F})\) such that \(X\) is a \(v\)-element set and \({\mathcal F}\) is a family of \(k\)-element subsets, called blocks, of \(X\) with the property that every pair of distinct elements of \(X\) is contained in at least one block.
Chee, Yeow Meng, Ling, San
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Ramified cover of varieties with nef cotangent bundle
Comptes Rendus. Mathématique, 2022 We construct examples to show that having nef cotangent bundle is not preserved under finite ramified covers. Our examples also show that a projective manifold with Stein universal cover may not have nef cotangent bundle, disproving a conjecture of Liu ...
Wang, Yiyu
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Covers and Envelopes by Submodules or Quotient-Modules
Journal of Mathematics, 2023 Let R be a ring, X a class of left R-modules, S the class of submodules of X, and Q the class of quotient-modules of X. It is shown that SQ is precovering (preenveloping) if and only if every injective (projective) left R-module has an X-precover (X ...
Yuedi Zeng
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Journal of Mathematics, 2022 In this paper, we investigate the notions of X⊥-projective, X-injective, and X-flat modules and give some characterizations of these modules, where X is a class of left modules. We prove that the class of all X⊥-projective modules is Kaplansky.
Arunachalam Umamaheswaran +4 more
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Projective covers over local rings [PDF]
Annali di Matematica Pura ed Applicata (1923 -), 2021 AbstractWe describe the structure of the projective cover of a module $$M_R$$ M R over a local ring R and its relation with minimal sets of generators of $$M_R$$ M R
Ercolanoni S., Facchini A.
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