×

The degrees of regularity in varieties. (English) Zbl 0955.08005

Summary: Congruence regular varieties are characterized by a Mal’tsev condition containing \(m\)-ary terms. We prove that this number \(m\) is the degree of regularity, i.e. the number of elements which generate the congruence class of every principal congruence.

MSC:

08B05 Equational logic, Mal’tsev conditions
08A30 Subalgebras, congruence relations
PDFBibTeX XMLCite
Full Text: EuDML

References:

[1] Barbour G. D., Raftery J. G.: On the degrees of permutability of subregular varieties. preprint 1994. · Zbl 0927.08001
[2] Chajda I.: Regularity and permutability of congruences. Algebra Univ. 11 (1980), 159-162. · Zbl 0449.08007
[3] Duda J.: Maľcev condition for regular and weakly regular subalgebras of the square. Acta Sci. Math. (Szeged) 46 (1983), 29-34. · Zbl 0533.08002
[4] Duda J.: Maľcev conditions for subalgebras algebras. Acta Sci. Math. (Szeged) 51 (1987), 329-334.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.