Talk:Jacobson radical

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Isn't this list somewhat redundant? A left primitive ideal is the same thing as the annihilator of a simple left module.

Waltpohl 04:57, 24 Feb 2004 (UTC)

Two quotes from the text:

- The Jacobson radical of any field is {0}. The Jacobson radical of the integers is {0}.

- Unless R is the trivial ring {0}, the Jacobson radical is always a proper ideal in R

{0} is not a proper ideal. A field is not the trivial ring. What is going on? Juryu 16:28, 25 February 2006 (UTC)

Proper ideal of ring R here is evidently being used to mean ideal not equal to R.--CSTAR 17:02, 25 February 2006 (UTC)

[edit] Rings without identity

Listed under 'Properties' is this statement: "Unless R is the trivial ring {0}, the Jacobson radical is always an ideal in R distinct from R". The Jacobson radical of R may be equal to R in a ring without identity. -- Heath 69.174.67.197 15:14, 11 October 2006 (UTC)