Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I am new to semigroup research, so I apologize if this is an easy question.

share|improve this question
add comment

1 Answer

Assuming by M(n, Z) you mean the semigroup (monoid) of n × n matrices over the integers under multiplication: no, it is not even finitely generated, because the determinant M(n, Z) → Z is multiplicative (Z denoting the monoid of integers under multiplication) and Z is not finitely generated (by the infinitude of primes).

share|improve this answer
3  
If n=0, then M(n,Z) is finitely presented! (Sorry for being obnoxious.) –  Bjorn Poonen Feb 10 '10 at 8:33
add comment

Your Answer

 
discard

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.