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

Is the unimodular row $(x,y,z)$ completable over the ring $({\mathbb Z}/2{\mathbb Z})[x,y,z,y',z']/\langle x^2+yy'+zz'-1 \rangle$ ?

share|improve this question
1  
A good strategy for getting an answer is defining the terms you are using. What is a unimodular row, what is completable? –  Franz Lemmermeyer May 28 '11 at 13:35
1  
Also you should post your own ideas / approaches, etc. –  Martin Brandenburg May 28 '11 at 13:47
    
In other words, can we find $p_1,p_2,p_3,q_1,q_2,q_3 \in (\mathbb{Z}/2\mathbb{Z})[x,y,z,y',z'] $ such that $$\begin{array}{|ccc|}x &p_1&q_1\\ y&p_2&q_2\\ z &p_3&q_3\\ \end{array} \equiv 1 \; \mod \; \langle x^2+yy'+zz'-1\rangle \; ?$$ –  user15425 Jun 3 '11 at 17:02

1 Answer 1

Your question is equivalent to the $n=2$ case of what T.Y. Lam calls "Murthy's $(a,b,c)$ problem" in his book "Serre's problem on projective modules. (This is statement 5.7 on p. 323 in the 2006 edition).

Lam indicates that this is wide open.

share|improve this answer

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.