Related papers: Metric freedom and projectivity for classical and …

In the last few years, Lopez-Permouth and several collaborators have introduced a new approach in the study of the classical projectivity, injectivity and flatness of modules. This way, they introduced subprojectivity domains of modules as…

We show that the cyclic and epicyclic categories which play a key role in the encoding of cyclic homology and the lambda operations, are obtained from projective geometry in characteristic one over the infinite semifield F of "max-plus…

This expository note delves into the theory of projective modules parallel to the one developed for injective modules by Matlis. Given a perfect ring $R$, we present a characterization of indecomposable projective $R$-modules and describe a…

Projective modules play an important role in the study of the category of modules over rings and in the characterization of various classes of rings. Several characterizations of projective objects which are equivalent for modules over…

We describe rings over which every right module is almost injective. We give a description of rings over which every simple module is a almost projective.

In this paper we will study the homological properties of various natural modules associated to the Fourier algebra of a locally compact group. In particular, we will focus on the question of identifying when such modules will be projective…

Quantum measurements are ubiquitous in quantum information processing tasks, but errors can render their outputs unreliable. Here, we present a scheme that implements a robust projective measurement through measuring code-inspired…

Let $(R,\mm,K)$ be a regular local ring containing a field $k$ such that either char $k=0$ or char $k=p$ and tr-deg $K/\BF_p\geq 1$. Let $g_1,\ldots,g_t$ be regular parameters of $R$ which are linearly independent modulo $\mm^2$. Let…

In recent years, persistence modules have been viewed as graded modules with gradation over a preordered set serving as the indexing set. We provide sufficient criteria for a projective module over a PID to be free when the indexing set is…

Fix a manifold M, and let V be an infinite dimensional Lie algebra of vector fields on M. Assume that V contains a finite dimensional semisimple maximal subalgebra A, the projective or conformal subalgebra. A projective or conformal…

We generalize to quantum weighted projective spaces in any dimension previous results of us on K-theory and K-homology of quantum projective spaces `tout court'. For a class of such spaces, we explicitly construct families of Fredholm…

We introduce a weighted version of the module of logarithmic derivations of a divisor in weighted projective space, and provide a generalization of Saito's criterion for freeness in terms of weighted multiple eigenschemes (wME-schemes).…

Following a review of quantum-classical hybrid dynamics, we discuss the ensuing proliferation of observables and relate it to measurements of (would-be) quantum mechanical degrees of freedom performed by (would-be) classical ones (if they…

Drinfeld recently suggested to replace projective modules by the flat Mittag--Leffler ones in the definition of an infinite dimensional vector bundle on a scheme $X$. Two questions arise: (1) What is the structure of the class $\mathcal D$…

Projective metrics on vector spaces over finite fields, introduced by Gabidulin and Simonis in 1997, generalize classical metrics in coding theory like the Hamming metric, rank metric, and combinatorial metrics. While these specific metrics…

We introduce a framework for simulating quantum measurements based on classical processing of a set of accessible measurements. Well-known concepts such as joint measurability and projective simulability naturally emerge as particular cases…

Let $M$ be a finitely generated module over a local complete intersection $R$ of characteristic $p>0$. The property that $M$ has finite projective dimension can be characterized by the vanishing of $\ext_R^i({}^{f^n} R,M)$ for some $i>0$…

We show that there exists a fine moduli space for torsion-free sheaves on a projective surface, which have a "good framing" on a big and nef divisor. This moduli space is a quasi-projective scheme. This is accomplished by showing that such…

When deriving exact generalized master equations for the evolution of a reduced set of degrees of freedom, one is free to choose what quantities are relevant by specifying projection operators. However, obtaining a reduced description does…

We construct a new kind of measures, called projection families, which generalize the classical notion of vector and operator-valued measures. The maximal class of reasonable functions admits an integral with respect to a projection family,…