In this paper certain injectivity conditions in terms of extensions of monomorphisms are considered. In particular, it is proved that a ring R is a quasi-Frobenius ring if and only if every monomorphism from any essential right ideal of RR into R (N) R can be extended to RR. Also, known results on pseudo-injective modules are extended. Dinh raised the question if a pseudo-injective CS module is...

Proof: For f ∈ Hom(X,A), i ◦ f = 0 implies (i ◦ f)(x) = 0 for all x ∈ X, and then f(x) = 0 for all x since i is injective. Thus, Hom(X,A)→ Hom(X,B) is injective, giving exactness at the left joint. Since q ◦ i = 0, any f ∈ Hom(X,A) is mapped to 0 ∈ Hom(X,C) by f → q ◦ i ◦ f . That is, the image of i ◦ − is contained in the kernel of q ◦ −. On the other hand, when g ∈ Hom(X,B) is mapped to q ◦ g...

Abstract In finite group theory, chief factors play an important and well-understood role in the structure theory. We here develop a theory of for Polish groups. development this we prove version Schreier refinement theorem. also trichotomy topologically characteristically simple The requires two independently interesting lines study. First consider injective, continuous homomorphisms with dens...

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 prove a max-min theorem for weak containment in the context of algebraic actions. Namely, we show that given an action $G$ on $X,$ there is maximal, closed $G$-invariant subgroup $Y$ $X$ so weakly contained Bernoulli shift. This also minimal any shift $G\curvearrowright X/Y$-ergodic presence X$. give several applications, including major simplification proof measure entropy equals topologica...