Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Connected sums of Gorenstein local rings   A new construction of rings is introduced, studied, and applied. Given
surjective homomorphisms $R\to T\gets S$ of local rings, and ideals in $R$ and
$S$ that are isomorphic to some $T$-module $V$, the \emph{connected sum}
$R#_TS$ is defined to be the local ring obtained by factoring out the diagonal
image of $V$ in the fiber product $R\times_TS$. When $T$ is Cohen-Macaulay of
dimension $d$ and $V$ is a canonical module of $T$, it is proved that if $R$
and $S$ are Gorenstein of dimension $d$, then so is $R#_TS$. This result is
used to study how closely an artinian ring can be approximated by Gorenstein
rings mapping onto it. It is proved that when $T$ is a field the cohomology
algebra $\Ext^*_{R#_kS}(k,k)$ is an amalgam of the algebras $\Ext^*_{R}(k,k)$
and $\Ext^*_{S}(k,k)$ over isomorphic polynomial subalgebras generated by one
element of degree 2. This is used to show that when $T$ is regular, the ring
$R#_TS$ almost never is complete intersection.

24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an