Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Artinian algebras and Jordan type   The Jordan type of an element $\ell$ of the maximal ideal of an Artinian
k-algebra A acting on an A-module M of k-dimension n, is the partition of n
given by the Jordan block decomposition of the multiplication map $m_\ell$ on
M. In general the Jordan type has more information than whether the pair
$(\ell,M)$ is strong or weak Lefschetz. We develop basic properties of the
Jordan type and their loci for modules over graded or local Artinian algebras.
We as well study the relation of generic Jordan type of $A$ to the Hilbert
function of $A$. We introduce and study a finer invariant, the Jordan degree
type.
  In our last sections we give an overview of topics such as the Jordan types
for Nagata idealizations, for modular tensor products, and for free extensions,
including examples and some new results. We as well propose open problems.

23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat