Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The weak Lefschetz property for m-full ideals and componentwise linear
  ideals   We give a necessary and sufficient condition for a standard graded Artinian
ring defined by an m-full ideal, to have the weak Lefschetz property in terms
of graded Betti numbers. This is a generalization of a theorem of Wiebe for
componentwise linear ideals. We also prove that the class of componentwise
linear ideals and that of completely m-full ideals coincide in characteristic
zero and in positive characteristic, with the assumption that the generic
initial ideal w.r.t. the graded reverse lexicographic order is stable.

34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph