1. Let R be a ring with unity. An R-module M is said to be balanced or to have the double centralizer property, if the natural homomorphism from R to the double centralizer of M is surjective. If all left and right K-modules are balanced, R is called balanced. It is well known that every artinian uniserial ring is balanced. In [5], J. P. Jans conjectured that those were the only (artinian) bala...

Given a ring homomorphism B → A, consider its centralizer R = A, bimodule endomorphism ring S = EndBAB and sub-tensor-square ring T = (A ⊗B A) B . Nonassociative tensoring by the cyclic modules RT or SR leads to an equivalence of categories inverse to the functors of induction of restricted A-modules or restricted coinduction of B-modules in case A |B is separable, H-separable, split or left de...

To classify the finite dimensional pointed Hopf algebras with Weyl group G of E8, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. In this paper we only list character table 95–112. 2000 Mathematics Subject Classification: 16W30, 68M07 keywords: GAP, Hopf algebra, Weyl group, character. 0. Introdu...

To classify the finite dimensional pointed Hopf algebras with Weyl group G of E8, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. In this paper we only list character table 65–94. 2000 Mathematics Subject Classification: 16W30, 68M07 keywords: GAP, Hopf algebra, Weyl group, character. 0. Introduc...

To classify the finite dimensional pointed Hopf algebras with Weyl group G of E8, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. In this paper we only list character table 29–46. 2000 Mathematics Subject Classification: 16W30, 68M07 keywords: GAP, Hopf algebra, Weyl group, character. 0. Introduc...

To classify the finite dimensional pointed Hopf algebras with Weyl group G of E8, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. In this paper we only list character table 47–64. 2000 Mathematics Subject Classification: 16W30, 68M07 keywords: GAP, Hopf algebra, Weyl group, character. 0. Introduc...

Background and purpose - A tapered, polished and collarless stem is normally equipped with a hollow centralizer to prevent the stem from becoming end-bearing in the cement as the stem subsides. In a randomized clinical trial, we evaluated such a stem (MS-30), which was initially introduced with a solid centralizer but was later recommended to be fitted with a hollow centralizer. We hypothesized...

Normalizers and p-normalizers of maximal tori in p-compact groups can be characterized by the Euler characteristic of the associated homogeneous spaces. Applied to centralizers of elementary abelian p-groups these criteria show that the normalizer of a maximal torus of the centralizer is given by the centralizer of a preferred homomorphism to the normalizer of the maximal torus; i.e. that “norm...