Based on a description of the squares of cofinite primary ideals of A + α (D), we prove the following results: for α ≥ 1, there exists a derivation from A + α (D) into a finite-dimensional module such that this derivation is unbounded on every dense subalgebra; for m ∈ N and α ∈ [m, m + 1), every finite-dimensional extension of A + α (D) splits algebraically if and only if α ≥ m + 1/2.

Let m ≥ 1 be a positive integer. We show that, over an algebraically closed field of characteristic zero, there exists cosemisimple Hopf algebras having an antipode of order 2m. We also discuss the Schur indicator for such Hopf algebras.

Abstract Let G be a simple algebraic group of adjoint type over an algebraically closed field k bad characteristic. We show that its sheets conjugacy classes are parametrized by -conjugacy pairs $(M,{\mathcal O})$ where M is the identity component centralizer semisimple element in and ${\mathcal O}$ rigid unipotent class , analogy with good characteristic case.

We describe the structure of 0-simple countably compact topological inverse semigroups and the structure of congruence-free countably compact topological inverse semigroups. We follow the terminology of [3, 4, 8]. In this paper all topological spaces are Hausdorff. If S is a semigroup then we denote the subset of idempotents of S by E(S). A topological space S that is algebraically a semigroup ...

We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder’s theorem. We also prove that the spectral mapping theorem holds for the Drazin spectrum and for analytic functions on an open neighborhood of σ(T ). As applications, we show that if T is algebraically M -hyponormal, or if T is algebraically paranormal, then the generalized Weyl’s theore...

Introduction Recall that for proper smooth and connected curves of genus g ≥ 2 over an algebraically closed eld of characteristic 0 the structure of the étale fundamental group π g is well known and depends only on the genus g. Namely it is the pro-nite completion of the topological fundamental group of a compact orientable topological surface of genus g. In contrast to this, the structure of t...

A group G is called to be acceptable (due M. Larsen) if for any finite H, two element-conjugate homomorphisms are globally conjugate. We prove that semisimple algebraic over an algebraically closed field of non-zero characteristics not acceptable.