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 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 ...

The interactions between topological covering spaces, homotopy and group structures in a fibered space exhibit an array of interesting properties. This paper proposes the formulation finite components compact Lindelof variety (C, R) spaces. spaces form Noetherian structure under injective embeddings. locally path-connected establish set groups, maintaining homomorphism. homeomorphic embedding b...

We characterize the category of injective *-homomorphisms between commutative C*-subalgebras of various C*-algebras, namely C*-algebras of operators on separable Hilbert spaces, any finite-dimensional C*-algebra, and any commutative C*-algebra.

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 the...

We claim that monomorphisms in Sets and Groups are the usual injective maps and homomorphisms. First, suppose that f : A → B is a set injection and that fg = gh. Then for all c ∈ C, we have f(g(c)) = f(h(c)) implies g(c) = h(c) by injectivitiy. Hence g = h. Conversely, suppose f : A → B is not an injection. Then let f(a) = f(a′) for some a 6= a′ ∈ A. Then let g(c) = a and h(c) = a′ for all c ∈ ...

It is proved that localizations of injective R-modules of finite Goldie dimension are injective if R is an arithmetical ring satisfying the following condition: for every maximal ideal P , RP is either coherent or not semicoherent. If, in addition, each finitely generated R-module has finite Goldie dimension, then localizations of finitely injective R-modules are finitely injective too. Moreove...

Abstract Assume that k is an algebraically closed field and A a finite-dimensional wild -algebra. Recently, L. Gregory M. Prest proved in this case the width of lattice all pointed -modules undefined. Hence result Ziegler implies there exists super-decomposable pure-injective -module, if base countable. Here we give different straightforward proof fact. Namely, show special family -modules, cal...

Let A and B be C*-algebras $$\varphi :A\rightarrow B$$ a $$*$$ -homomorphism. We discuss the properties of kernel (co-)image induced map $$\mathrm {K}_{0}(\varphi ):\mathrm {K}_{0}(A) \rightarrow \mathrm {K}_{0}(B)$$ on level K-theory. In particular, we are interested in case that co-image is torsion free, show it holds when commutative unital, has real rank zero, $$ unital injective. also embe...