Journal of Algebra, Number Theory: Advances and ApplicationsAuthor's: Alberto Chicco
Pages: [41] - [82]
Received Date: June 21, 2019
Submitted by:
DOI: http://dx.doi.org/10.18642/jantaa_7100122076
The aim of this paper is to present some new results concerning the
property of congruence n-permutability for varieties of
algebras. The first of such results is a new termwise characterization
of congruence n-permutability, obtained by using some relations
with particular configurations. Indeed, the shapes of these relations
have inspired the definition of what we have called special
Hagemann relations of dimension 
briefly 
for fixed 
the class of varieties that omit 
turns out to be a prime Maltsev filter within
the lattice of interpretability types (see [5]). Finally, by still
using the special Hagemann relations, we provide some arguments for
the primeness of:
(1) congruence 2-permutability with respect to idempotent
varieties;
(2) congruence 3-permutability with respect to idempotent locally
finite varieties (more thoroughly discussed in [3]);
(3) congruence n-permutability, for some 
with respect to idempotent varieties.
congruence n-permutable variety, idempotent, Maltsev condition, prime, special Hagemann relation.
