For a long period the theory of modules over rings on the one hand and comodules and Hopf modules for coalgebras and bialgebras on the other side developed quite independently. In this talk we want to outline how ideas from module theory can be applied to enrich the theory of comodules and vice versa. For this we consider A-corings C with grouplike elements over a ring A, in particular Galois c...

We analyze the geometry of the Ext-quiver of a coalgebra C in order to study the behavior of simple and injective C-comodules under the action of the functors associated to a localizing subcategory of the category of C-comodules.

The concepts of free modules, projective modules, injective modules, and the like form an important area in module theory. The notion of free fuzzy modules was introduced by Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameri introduced the concept of projective and injective L-modules. In this paper, we give an alternate definition for injective L-modules and prove t...

We consider the ideal structure of a reduced crossed product unital C∗-algebra equipped with an action discrete group. More specifically we find sufficient and necessary conditions for group to have intersection property, meaning that non-zero ideals in restrict underlying C∗-algebra. show property on is equivalent equivariant injective envelope. also centre envelope always contains C∗-algebrai...

(ii) Denote this map by φ, which is induced by the compositions with εi : Xi ↪→ ⊔ j Xj , i ∈ I. If φ(fi) = φ(gj) for some fi ∈ Hom(Y,Xi) and gj ∈ Hom(Y,Xj), then we must have i = j because φ(fi) and φ(gj) have the same image. Since φ(fi) = εi ◦ fi, φ(gi) = εi ◦ gi and εi is an injective map, we deduce that fi(y) = gi(y), ∀y ∈ Y , i.e. fi = gi. (iii) This map is induced by the composition with t...

We introduce the notion of integrality Grothendieck categories as a simultaneous generalization primeness noncommutative noetherian rings and locally schemes. Two different spaces associated to category yield respective definitions integrality, we prove equivalence these using Grothendieck-categorical version Gabriel's correspondence, which originally related indecomposable injective modules pr...

In this paper we prove that the 3-fold injective tensor product ℓ1⊗ˆεℓ1⊗ˆεℓ1 is not isomorphic to any subspace of ℓ1⊗ˆεℓ1. This result provides a new solution problem Diestel on projective products c0. Moreover, implies for infinite countable compact metric space K, C(K)⊗ˆπC(K)⊗ˆπC(K) quotient C(K)⊗ˆπC(K).

Codes Description of C Nonsingular C injective – i.e. ∀x, x′ ∈ X , x 6= x′ =⇒ C(x) = C(x′) Uniquely Decodable The extension the code is nonsingular. Prefix/Instantaneous/Self-punctuating No code word prefixes another: for all distinct x′, x′′ ∈ X , C(x′) does not start with C(x′′) We illustrate this below with the following example for the symbols {a, b, c, d} taken from Chapter 5 in Cover and ...