Friday, August 29, 2008

Radical Times

Ok, at the moment I'm trying to characterise the Jacobson radical of the factor algebra of the algebra of complex functions from a ring under multiplicative convolution. If you think that sounds convoluted I probably shouldn't add that this was the simplest explanation I could come up with. I've typed up a rough sketch of some of the background work I've done on this algebra, what it is and how it works. The Jacobson radical however is proving elusive, despite all my best efforts. Essentially I've a big set of objects with some structure and I'm trying to find a little very structured bit inside it that has special properties. Tricky stuff :) Hopefully once I've found out what it looks like I'll be able to use it to prove a theorem that another researcher in the field has already proved a different way. Made especially difficult since I can't seem to find his proof or any mention of it.

Also, I've been aksed to review an article on an area related to mine for a recognised journal. Unfortunately I've not much experience with this area which means an awful lot of background reading. I don't think my review will be up to much although I think I've found a neater way to define one of the objects they use. My lack of global vision on the topic precludes any idea of the overall relevence of the work.