We investigate categorical versions of algebraically closed (= pure) embeddings, existentially closed embeddings, and the like, in the context of locally presentable categories. The definitions of S. Fakir [Fa, 75], as well as some of his results, are revisited and extended. Related preservation theorems are obtained, and a new proof of the main result of Rosický, Adámek and Borceux ([RAB, 02])...

In this paper we introduce a generalization of M-small modules and discuss about the torsion theory cogenerated by this kind of modules in category . We will use the structure of the radical of a module in  and get some suitable results about this class of modules. Also the relation between injective hull in  and this kind of modules will be investigated in this article.   For a module  we show...

we show that the character space of the vector-valued lipschitz algebra $lip^{alpha}(x, e)$ of order $alpha$ is homeomorphic to the cartesian product $xtimes m_e$ in the product topology, where $x$ is a compact metric space and $e$ is a unital commutative banach algebra. we also characterize the form of each character on $lip^{alpha}(x, e)$. by appealing to the injective tensor product, we then...

‎Let $M$ be a non-zero finitely generated module over a commutative Noetherian local ring $(R,mathfrak{m})$ with $dim_R(M)=t$‎. ‎Let $I$ be an ideal of $R$ with $grade(I,M)=c$‎. ‎In this article we will investigate several natural homomorphisms of local cohomology modules‎. ‎The main purpose of this article is to investigate when the natural homomorphisms $gamma‎: ‎Tor^{R}_c(k,H^c_I(M))to kotim...

An injective coloring of a graph is a vertex labeling such that two vertices sharing a common neighbor get different labels. In this work we introduce and study what we call additive colorings. An injective coloring c : V (G) → Z of a graph G is an additive coloring if for every uv, vw in E(G), c(u)+ c(w) = 2c(v). The smallest integer k such that an injective (resp. additive) coloring of a give...

We give a characterization of all cartesian products D1×D2 ⊂ C for which the Lempert function and the injective Lempert function coincide. In particular, we show that there exist domains in C for which they are different.

Let $P$ be a submonoid of group $G$ and let $\mathcal{E}=(\mathcal{E}_p)_{p\in P}$ product system over with coefficient C*-algebra $A$. We show that the following C*-algebras are canonically isomorphic: C*-envelope tensor algebra $\mathcal{T}_\lambda(\mathcal{E})^+$ $\mathcal{E}$; reduced cross sectional Fell bundle associated to canonical coaction on covariance $A\times_{\mathcal{E}}P$ cosyste...

Let X be a countable fundamental set in a Hilbert space H, and let T be the operator X x2X c(x)x: Whenever T is well-deened and bounded, X is said to be a Bessel sequence. If, in addition, ran T is closed, then X is a frame. Finally, a frame whose corresponding T is injective is a stable basis (also known as a Riesz basis). This paper considers the above three properties for subspaces H of L 2 ...

let $pounds$ be the category of locally compact abelian groups and $a,cin pounds$. in this paper, we define component extensions of $a$ by $c$ and show that the set of all component extensions of $a$ by $c$ forms a subgroup of $ext(c,a)$ whenever $a$ is a connected group. we establish conditions under which the component extensions split and determine lca groups which are component projective. ...

Let U be the set of prime ideals P completion a Stanley–Reisner ring S, such that localization at Frobenius algebra injective hull residue field S is finitely generated algebra. We give partial answer to conjecture made by M. Katzman about openness U. Specifically, we show has non-empty interior and present some sufficient conditions for principal open D(f) contained in U, intersections closed ...