Polynomial constraints for finiteness of semisimple rings

Mohan S. Putcha and Adil Mohamed Yaqub

Vol. 57 (1975), No. 2, 519–530

DOI: 10.2140/pjm.1975.57.519

Abstract

Suppose R is an associative ring with Jacobson radical J. Suppose that for each sequence x₁,⋯,x_n in R there exists a polynomial p homogeneous (of bounded degree) in each x_i and a monomial w in the x’s, in which some x_t is missing, such that p = w. Then R∕J is finite. It is also shown that if the above polynomial p is a monomial, then R∕J is finite and J is nil of bounded index.

Mathematical Subject Classification

Primary: 16A40

Milestones

Received: 18 October 1974

Published: 1 April 1975