Projects per year
Abstract
A result of Bergman says that the Jacobson radical of a graded algebra is homogeneous. It is shown that while graded Jacobson radical algebras have homogeneous elements nilpotent, it is not the case that graded algebras all of whose homogeneous elements are nilpotent are Jacobson radical. To contrast this, the following result of the author is slightly extended. Let R be a graded algebra generated in the degree one. If for every n, the n x n matrix algebra over R has all homogeneous elements nilpotent, then R is Jacobson radical.
Original language  English 

Pages (fromto)  917928 
Number of pages  12 
Journal  Bulletin of the london mathematical society 
Volume  40 
DOIs  
Publication status  Published  Dec 2008 
Keywords
 NOETHERIANRINGS
 NIL
 ALGEBRAS
 DIMENSION
Projects
 1 Finished

Nil algebras, algebraic algebras and algebras with finite GelfandKirillov dimension
1/08/06 → 31/07/11
Project: Research