On quotient-fields generated by pseudonormed rings

Commutative Rings with Finite Quotient Fields

We consider the class of all commutative reduced rings for which there exists a finite subset T ⊂ A such that all projections on quotients by prime ideals of A are surjective when restricted to T . A complete structure theorem is given for this class of rings, and it is studied its relation with other finiteness conditions on the quotients of a ring over its prime ideals. Introduction Our aim i...

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...

Generalized Quotient Rings

On infinitesimal ~-fields generated by random processes

Let X(t) , t >1 O, be a Polish space-valued r a n d o m process defined on a probabi l i ty space (~, ~ , P), where ~ is the P-comple t ion of a countab ly generated a-field ~ o . Let ~(t + ) (the ' l ook-ahead ' a-field at t) and r ) (the ' l ook-back ' a-field at t) denote the P-comple t ions of c~>,a(X(y), t <~ y <~ s) and c~s<ta(X(y), s ~< y ~< t) respectively. The aim of this note is to p ...

Stable Rings Generated by Their Units

We introduce the class of rings satisfying (m,1)-stable range and investigate equivalent characterizations of such rings. These give generalizations of the corresponding results by Badawi (1994), Ehrlich (1976), and Fisher and Snider (1976). 2000 Mathematics Subject Classification. 19B10, 16E50. Let R be an associative ring with identity. A ring R is said to have stable range one provided that ...