Jacobson - rings and hilbert algebras with polynomial identities

Summary We consider n-tuples of m × m matrices as zeroes of non-commutative polynomials in n-variables and establish an analogue of the classical Hilbert-Nullstellensatz. We study then finitely generated non-commutative algebras over Jacobson rings and obtain results conpletely analogous with the commutative tehory. In memory of Guido Castelnuovo, in the recurrence of the first centenary of his birth. Done partly under NSF Senior Foreign Scientist Fellowship at the Univ. of Chicago. The second named author has been supported by an A.R.O. grant n^o DA-ARO-D-31-124-G 501 at the Univ. of Chicago.     

The Jacobson Radical of （R[G]）^G

In this paper,the Jacobson radical of (R[G])G, the fixed point subring of a group ring (R[G]) is studied. Some related properties of (R[G])G are discussed.     

Jack Howlett, 1912-1999

Dr Jack Howlett, who died on 5 May 1999 at the age of 86, aFounder Fellow of the Institute of Mathematics and its Applications,was a mathematician with a special interest in numerical analysiswho early recognised the power of computing methods and whostrongly influenced the development of some mechanical computingmachines and electronic computers as we know them today. Thewidespread advance of the use of computer models in all scientificdisciplines was made possible thanks to the efforts of a smallnumber of mathematicians who laid the foundations of modernnumerical analysis during the late 1930s to early 1960s, a periodwhich covered the greater part of Jack's working life and inwhich he was a star player.