MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Is there a name for finite-dimensional associative $F$-algebras having the Jacobson radical of codimension 1. Of course they are particular local algebras and, indeed, the converse is true provided $F$ is algebraically closed.

share|cite|improve this question
up vote 2 down vote accepted

Those are local basic algebras.

share|cite|improve this answer
A finite dimensional algebra is basic if modulo its radical is a direct product of copies of the base field, and in that case it is local iff there is exactly one factor. – Mariano Suárez-Alvarez Apr 20 '13 at 16:12
Thank you very much! – Sammy Apr 20 '13 at 17:36
Some people would say split basic and use basic for the radical quotient being a direct product of division rings. – Benjamin Steinberg Apr 20 '13 at 18:07

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.