In this paper we exhibit some examples of non-Gorenstein Hecke algebras, and hence some modular forms for which mod 2 multiplicity one does not hold. Define S2(Γ0(N)) to be the space of classical cuspidal modular forms of weight 2, level N , and trivial character. The Hecke algebra TN is defined to be the subring of End(S2(Γ0(N)) generated by the Hecke operators {Tp : p 6 |N} and {Uq : q|N}. Le...

A generalization of injective modules (noted GI-modules), distinct from p-injective modules, is introduced. Rings whose p-injective modules are GI are characterized. If M is a left GI-module, E = End(AM), then E/J(E) is von Neumann regular, where J(E) is the Jacobson radical of the ring E. A is semisimple Artinian if, and only if, every left A-module is GI. If A is a left p. p., left GI-ring su...

This is a report for my presentation at the upcoming meeting on Berechenbarkeitstheorie (“Computability Theory”), Oberwolfach, January 21–27, 2001. We use 2 to denote the space of infinite sequences of 0’s and 1’s. For X, Y ∈ 2, X ≤T Y means that X is Turing reducible to Y . For P,Q ⊆ 2 we say that P is Muchnik reducible to Q, abbreviated P ≤w Q, if for all Y ∈ Q there exists X ∈ P such that X ...

The aim of this paper is to investigate some properties of pre-I-open sets, semi-I-open sets and b-I-open sets in ideal topological spaces. Some relationships of pre-I-open sets, semi-I-open sets and b-I-open sets in ideal topological spaces are discussed. Moreover, decompositions of continuity are provided. 2000 Mathematics Subject Classification: 54A05, 54A10, 54C08, 54C10.

let $r$ be a commutative noetherian ring with non-zero identity and $fa$ an ideal of $r$. let $m$ be a finite $r$--module of finite projective dimension and $n$ an arbitrary finite $r$--module. we characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(m,n)$ in certain serre subcategories of the category of modules from upper bounds. we define and study the properti...

To a Hecke symmetry R there associate the matrix bialgebra ER and the matrix Hopf algebra HR, which are called function rings on the matrix quantum semi-group and matrix quantum groups associated to R. We show that for an even Hecke symmetry, the rational representations of the corresponding quantum group are absolutely reducible and compute the integral on the function ring of the quantum grou...

In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric.In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fi...

We consider a special case of the problem of computing the Galois group of a system of linear ordinary differential equations Y ′ = MY, M ∈ C(x)n×n. We assume that C is a computable, characteristic-zero, algebraically closed constant field with factorization algorithm. There exists a decision procedure, due to Compoint and Singer, to compute the group in case the system is completely reducible....

Let M be a simple manifold, and F be a component of ∂M of genus two. For a slope γ on F , we denote by M(γ) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of γ on F . In this paper, we shall prove that there is at most one separating slope γ on F so that M(γ) is ∂-reducible.