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...

Let R be a ring with identity and C(R) denote the category of complexes of R-modules. In this paper we study the homotopy categories arising from projective (resp. injective) complexes as well as Gorenstein projective (resp. Gorenstein injective) modules. We show that the homotopy category of projective complexes over R, denoted K(Prj C(R)), is always well generated and is compactly generated p...

We give sharp conditions on a local biholomorphism F : X → C n which ensure global injectivity. For n ≥ 2, such a map is injective if for each complex line l ⊂ C n , the pre-image F −1 (l) embeds holomorphically as a connected domain into CP 1 , the embedding being unique up to Möbius transformation. In particular, F is injective if the pre-image of every complex line is connected and conformal...

We prove the following: 1. Let ǫ > 0 and let S1, S2 be two closed hyperbolic surfaces. Then there exists locallyisometric covers S̃i of Si (for i = 1, 2) such that there is a (1 + ǫ) bi-Lipschitz homeomorphism between S̃1 and S̃2 and both covers S̃i (i = 1, 2) have bounded injectivity radius. 2. Let M be a closed hyperbolic 3-manifold. Then there exists a map j : S → M where S is a surface of bound...

We consider a symmetric monoidal closed category V = (V ,⊗, I, [−,−]) together with a regular injective object Q such that the functor [−, Q] : V → V op is comonadic and prove that in such a category, as in the monoidal category of abelian groups, a morphism of commutative monoids is an effective descent morphism for modules if and only if it is a pure monomorphism. Examples of this kind of mon...

It is well-known that the topological boundary of the spectrum of an operator is contained in the approximate point spectrum. We show that the one-sided version of this result is not true. This gives also a negative answer to a problem of Schmoeger. Denote by L(X) the algebra of all bounded linear operators acting in a Banach space X. For T ∈ L(X) denote by σ(T ), σl(T ) and σπ(T ) the spectrum...

We examine the question of when the ∗–homomorphism λ : A ∗D B → Ã ∗ D̃ B̃ of full amalgamated free product C∗–algebras, arising from compatible inclusions of C∗–algebras A ⊆ Ã, B ⊆ B̃ and D ⊆ D̃, is an embedding. Results giving sufficient conditions for λ to be injective, as well of classes of examples where λ fails to be injective, are obtained. As an application, we give necessary and sufficient ...

In the present paper, we study certain quotients of étale fundamental group a hyperbolic curve over field. We prove that action outer automorphism quotient an algebraically closed field on its conjugacy classes open subgroups is faithful. Also, that, if k either number or p-adic local field, then Galois representation associated to geometric ℙk1\{0,1,∞} injective.

We investigate finitary functions from [Formula: see text] to for a square-free number text]. show that the lattice of all clones on set which contain addition is finite. provide an upper bound cardinality this through injective function direct product lattices text]-linearly closed clonoids, text], power, where These are studied in [S. Fioravanti, Closed sets between products finite fields pai...