0
$\begingroup$

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

$\endgroup$
3
  • 1
    $\begingroup$ A good strategy for getting an answer is defining the terms you are using. What is a unimodular row, what is completable? $\endgroup$ May 28, 2011 at 13:35
  • 1
    $\begingroup$ Also you should post your own ideas / approaches, etc. $\endgroup$ May 28, 2011 at 13:47
  • $\begingroup$ 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 $$\begin{array}{|ccc|}x &p_1&q_1\\ y&p_2&q_2\\ z &p_3&q_3\\ \end{array} \equiv 1 \; \mod \; \langle x^2+yy'+zz'-1\rangle \; ?$$ $\endgroup$
    – user15425
    Jun 3, 2011 at 17:02

1 Answer 1

2
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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