Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rosenberg's classification of maximal clones   We give a proof of I. G. Rosenberg's characterization of maximal clones. The
theorem lists six types of relations on a finite set such that a clone over
this set is maximal if and only if it contains just the functions preserving
one of the relations of the list. In Universal Algebra, this translates
immediately into a characterization of the finite preprimal algebras: A finite
algebra is preprimal if and only if its term operations are exactly the
functions preserving a relation of one of the six types listed in the theorem.
The difficult part of the proof is to show that all maximal clones or preprimal
algebras respectively are of that form. This follows from, and, as we also
demonstrate, is indeed equivalent to, a characterization of primal algebras: We
show that the primal algebras are exactly those whose term operations do not
preserve any of the relations on the list.

22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ