We study finite dimensional representations over some Noetherian algebras a field of characteristic zero. More precisely, we give necessary and sufficient conditions for the category locally to be closed under taking injective hulls extend results known group rings enveloping Ore extensions, Hopf crossed products, affine low Gelfand-Kirillov dimension.

let r be a commutative noetherian ring. we study the behavior of injectiveand at dimension of r-modules under the functors homr(-,-) and -×r-.

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...

In this note, we give an explicit counterexample to the simple loop conjecture for representations of surface groups into PSL(2, R). Specifically, we use a construction of DeBlois and Kent to show that for any orientable surface with negative Euler characteristic and genus at least 1, there are uncountably many non-conjugate, non-injective homomorphisms of its fundamental group into PSL(2, R) t...

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...

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...

The present study investigates some novel categorical properties of soft sets. By combining categorical theory with soft set theory, a categorical framework of soft set theory is established. It is proved that the category SFun of soft sets and soft functions has equalizers, finite products, pullbacks, and exponential properties. It is worth mentioning that we find that SFun is both a topologic...