# Completion of unimodular rows

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

-
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
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

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).