Two-Sided Semisimple Maximal Quotient Rings

Two-sided Grassmann-Rayleigh quotient iteration

The two-sided Rayleigh quotient iteration proposed by Ostrowski computes a pair of corresponding left-right eigenvectors of a matrix C. We propose a Grassmannian version of this iteration, i.e., its iterates are pairs of p-dimensional subspaces instead of one-dimensional subspaces in the classical case. The new iteration generically converges locally cubically to the pairs of left-right p-dimen...

Filtrations in Semisimple Rings

In this paper, we describe the maximal bounded Z-filtrations of Artinian semisimple rings. These turn out to be the filtrations associated to finite Z-gradings. We also consider simple Artinian rings with involution, in characteristic 6= 2, and we determine those bounded Z-filtrations that are maximal subject to being stable under the action of the involution. Finally, we briefly discuss the an...

Semisimple Strongly Graded Rings

Let G be a finite group and R a strongly G-graded ring. The question of when R is semisimple (meaning in this paper semisimple artinian) has been studied by several authors. The most classical result is Maschke’s Theorem for group rings. For crossed products over fields there is a satisfactory answer given by Aljadeff and Robinson [3]. Another partial answer for skew group rings was given by Al...

Maximal Quotient Rings and Essential Right Ideals in Group Rings of Locally Finite Groups

MAXIMAL QUOTIENT RINGS AND ESSENTIAL RIGHT IDEALS IN GROUP RINGS OF LOCALLY FINITE GROUPS Theorem . zero . FERRAN CEDÓ * AND BRIAN HARTLEY Dedicated to the memory of Pere Menal Let k be a commutative field . Let G be a locally finite group without elements of order p in case char k = p > 0 . In this paper it is proved that the type I. part of the maximal right quotient ring of the group algebgr...

Generalized Quotient Rings