Related papers: Relative coherent modules

We formulate a notion of "geometric reductivity" in an abstract categorical setting which we refer to as adequacy. The main theorem states that the adequacy condition implies that the ring of invariants is finitely generated. This result…

n this article, firstly, we introduce the notion of star modules with respect to a balanced pair and obtain some properties. We mainly give the relationship between n-X star modules and n-X tilting modules [9], and a new characterization of…

We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…

In this work we study different classes of effective composite metrics proposed in the context of one-loop quantum corrections in bimetric gravity. For this purpose we consider contributions of the matter loops in form of cosmological…

The main purpose of this paper is to study complex valued metric-like spaces as an extension of metric-like spaces, complex valued partial metric spaces, partial metric spaces, complex valued metric spaces and metric spaces. In this…

We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…

We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…

Silting modules are abundant. Indeed, they parametrise the definable torsion classes over a noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also the universal localisations of a hereditary ring, or…

In this paper we lay the basis of the theory of rational modules of corings extending results on rational modules for coalgebras to the case of arbitrary ground rings. We apply these results mainly to categories of entwined modules (e.g.…

Here we show that the concepts behind such terms as entanglement, qubits, quantum gates, quantum error corrections, unitary time evolution etc., which are usually ascribed to quantum systems, can be adequately realized on a set of coupled…

A monoid $S$ is right coherent if every finitely generated subact of every finitely presented right $S$-act is finitely presented. The corresponding notion for a ring $R$ states that every finitely generated submodule of every finitely…

The article is developing homological algebra in modules over non-unital rings and algebras. The main application is the definition and study of (directed) homology of $(\infty,1)$-categories and of directed spaces, including relative…

Counterfactual reasoning is a foundational topic in both philosophical and logical studies \cite{Stalnaker1968-STAATO-5, Lewis1973-LEWC-2}. A pivotal component of counterfactual analysis is the concept of similarity between possible worlds…

Let $R$ be a commutative ring. We investigate $R$-modules which can be written as \emph{finite} sums of {\it {second}} $R$-submodules (we call them \emph{second representable}). We provide sufficient conditions for an $R$-module $M$ to be…

In this paper we describe how to give a particular global category of rings and modules the structure of a relaxed multi category, and we describe an algebra in this relaxed multi category such that vertex algebras appear as such algebras.

Researchers introduced the notion of j-Artinian rings in [3] and obtained significant results concerning this new class of rings. Motivated by their definition and findings, we extend the study to modules by introducing the concept of…

For a fixed ring, different classes of ring epimorphisms and localisation maps are compared. In fact, we provide sufficient conditions for a ring epimorphism to be a universal localisation. Furthermore, we consider recollements induced by…

The fundamental theorem of symmetric polynomials over rings is a classical result which states that every unital commutative ring is fully elementary, i.e. we can express symmetric polynomials with elementary ones in a unique way. The…

In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…

By Rickard's work, two rings are derived equivalent if there is a tilting complex, constructed from projective modules over the first ring such that the second ring is the endomorphism ring of this tilting complex. In this work I describe,…