Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An analogue of Hilbert's Syzygy Theorem for the algebra of one-sided
  inverses of a polynomial algebra   An analogue of Hilbert's Syzygy Theorem is proved for the algebra $\mS_n (A)$
of one-sided inverses of the polynomial algebra $A[x_1, ..., x_n]$ over an
arbitrary ring $A$: $$ \lgldim (\mS_n(A))= \lgldim (A) +n.$$ The algebra
$\mS_n(A)$ is noncommutative, neither left nor right Noetherian and not a
domain. The proof is based on a generalization of the Theorem of Kaplansky (on
the projective dimension) obtained in the paper. As a consequence it is proved
that for a left or right Noetherian algebra $A$: $$ \wdim (\mS_n(A))= \wdim (A)
+n.$$

22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics