On Modules with Few Minimax Cocentralizers

Let R be a ring and G a group. An R-module A is said to be minimax if A includes a noetherian submodule B such that A/B is artinian. The authors study a ?G-module A such that A/C _A (H) is minimax (as a ?-module) for every proper not finitely generated subgroup H.     

MTame Modules And Local Gabriel Correspondence

Using the concept of prime submodule for M ∈ R-Mod, P ∈ Spec(M), and N ∈ σ[M], we define when N is P-Mtame \ (Mtame) module. This concept generalizes the concept\ of P-tame (tame) modules. For M ∈ R-Mod and τ ∈M-tors, we use the concept of τ _M -Gabriel dimension and we study the relationship between Mtame modules and τ _M -Gabriel dimension. We find equivalent conditions for a module M progenerator in σ[M] with τ _M -Gabriel dimension to have τ _M -Gabriel correspondence in terms of the P-Mtame modules. This result extends the results by Albu et al. and Kim and Krause.     

A Braided Version of Some Results of Skryabin

We extend the main result of Skryabin in [9 Skryabin , S. ( 2007 ). Projectivity and freeness over comodule algebras . Trans. Amer. Math. Soc. 359 : 2597 – 2623 .[Crossref], [Web of Science ®] , [Google Scholar]] to Yetter-Drinfeld Hopf algebras over an arbitrary Hopf algebra H with bijective antipode.     

Finite-dimensional Representations for a Class of Generalized Intersection Matrix Lie Algebras

In this paper, the authors study a class of generalized intersection matrix Lie algebras gim(M_n), and prove that its every finite-dimensional semisimple quotient is of type M(n, a, c, d). Particularly, any finite dimensional irreducible gim(M_n) module must be an irreducible module of Lie algebra of type M(n, a, c, d) and any finite dimensional irreducible module of Lie algebra of type M(n, a, c, d) must be an irreducible module of gim(M_n).     

Tensor product of C-injective modules

The purpose of this paper is to calculate all the character tables of Hecke algebras associated with finite Chevalley groups of exceptional type and their maximal parabolic subgroups when they are commutative. In the case when the groups are of classical type, the character values of Hecke algebras are expressed by using the q-Krawtchouk polynomials and the q-Hahn polynomials (See [10] and [15]). On the other hand, the character tables of commutative Hecke algebras associated with exceptional Weyl groups and their maximal parabolic subgroups are given in [12]. In §1, we discuss the structure of Hecke algebras and in §2, we calculate all the character tables of these commutative Hecke algebras associated with finite Chevalley groups of exceptional type. Although some of them are well known, we include them for completeness     

On Crawley Modules

A curve Xis said to be of type (iV, γ) if it is an iV-sheeted covering of a curve of genus γ with at least one totally ramified point. A numerical semigroup His said to be of type (iV, γ) if it has γ positive multiples of Nin [N, 2N_J] such that its γth element is 2Nγ and (2γ+1)NεH. If the genus of X is large enough and N is prime, X is of type (TV, γ) if and only if there is a point P6 X such that the Weierstrass semigroup at P is of type (N, γ) (this generalizes the case of double coverings of curves). Using the proof of this result and the Buchweitz's semigroup, we can construct numerical semigroups that cannot be realized as Weierstrass semigroups although they might satisfy Buchweitz's criterion