Simple maximal quotient rings

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

Maximal Quotient Rings1

Let R be an associative ring in which an identity element is not assumed. A right quotient ring of P is an overring 5 such that for each aQS there corresponds rQR such that arQR and ar 9*0. A theorem of R. E. Johnson [l ] states that R possesses a right quotient ring S which is a (von Neumann) regular ring if and only if P has vanishing right singular ideal. In this case P possesses a unique (u...

The Maximal Free Rational Quotient

This short, expository note proves existence of the maximal quotient of a variety by free rational curves. 1. Definition of a maximal free rational quotient Definition 1.1. Let V be a Deligne-Mumford stack over a field k, and denote the smooth locus by V sm ⊂ V . A 1-morphism f : Pk → V sm is a free rational curve to V if fTV is generated by global sections and has positive degree. Let S be an ...

On Classical Quotient Rings of Skew Armendariz Rings

Let R be a ring, α an automorphism, and δ an α-derivation of R. If the classical quotient ring Q of R exists, then R is weak α-skew Armendariz if and only if Q is weak α-skew Armendariz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly ci...