Re: On the number of idempotent elements of a given ring

Based on some of the postings I've seen, it appears that to guarantee an
even number of idempotents we have to have a unique multiplicative
identity element, as in the ring described by Tobias Fritz. Odd
idempotent numbers become possible with no multiplicative identity
element (would the even integers count?) or with multiple multiplicative
identity elements like (1,x) in eclark's ring. So I stand
corrected/modified.

To Tobias Fritz: You sure that your "n=2" column corresponds to 2x2
matrices for all the listed k? I seem to find 24 idempotents for 2x2
matrices in Z_4, counting the zero and identity matrices plus 11
conjugate pairs having trace 1 and determinant 0.

--OL

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