Vol. 57, No. 2, 1975

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Polynomial constraints for finiteness of semisimple rings

Mohan S. Putcha and Adil Mohamed Yaqub

Vol. 57 (1975), No. 2, 519–530

Suppose R is an associative ring with Jacobson radical J. Suppose that for each sequence x1,,xn in R there exists a polynomial p homogeneous (of bounded degree) in each xi and a monomial w in the x’s, in which some xt 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
Received: 18 October 1974
Published: 1 April 1975
Mohan S. Putcha
Adil Mohamed Yaqub