Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Springer's odd degree extension theorem for quadratic forms over
  semilocal rings   A fundamental result of Springer says that a quadratic form over a field of
characteristic not 2 is isotropic if it is so after an odd degree extension. In
this paper we generalize Springer's theorem as follows. Let R be a an arbitrary
semilocal ring, let S be a finite R-algebra of constant odd degree, which is
{\'e}tale or generated by one element, and let q be a nonsingular R-quadratic
form whose base ring extension q S is isotropic. We show that then q is already
isotropic.

18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org