Geodesic
A Characterization of Varieties with a Difference Term, II: Neutral = Meet Semi-Distributive
Canadian mathematical bulletin, Tome 41 (1998) no. 3, pp. 318-327

Voir la notice de l'article provenant de la source Cambridge University Press

We provide more characterizations of varieties with a weak difference term and of neutral varieties. We prove that a variety has a (weak) difference term (is neutral) with respect to the $\text{TC}$ -commutator iff it has a (weak) difference term (is neutral) with respect to the linear commutator. We show that a variety $V$ is congruence meet semi-distributive iff $V$ is neutral, iff ${{M}_{3}}$ is not a sublattice of Con $\mathbf{A}$ , for $\mathbf{A}\in V$ , iff there is a positive integer $n$ such that $V{{\vDash }_{Con}}\alpha (\beta \,o\,\gamma )\le \alpha {{\beta }_{n}}$ .
DOI : 10.4153/CMB-1998-044-9
Mots-clés : 08B05, 08B99 
Lipparini, Paolo. A Characterization of Varieties with a Difference Term, II: Neutral = Meet Semi-Distributive. Canadian mathematical bulletin, Tome 41 (1998) no. 3, pp. 318-327. doi: 10.4153/CMB-1998-044-9
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[BS] [BS] Burris, S., Sankappanavar, H. P., A course in universal algebra. Springer, New York, 1981. Google Scholar

[Cz] [Cz] Czédli, G., A characterization of congruence semi-distributivity. In:UniversalAlgebra and Lattice Theory, Lecture Notes in Math. 1004(1983). Google Scholar

[He] [He] Herrmann, C., Affine algebras in congruence modular varieties. Acta Sci. Math. (Szeged) 41 (1979), 119–125. Google Scholar

[HMK] [HMK] Hobby, D., McKenzie, R., The structure of finite algebras. Contemp. Math. 76 (1988). Google Scholar

[Jo] [Jo] Jonsson, B., Congruence Varieties. Algebra Universalis 10 (1980), 355–394. Google Scholar

[Ke] [Ke] Kearnes, K. A., Commutator theory with a difference term. J.Algebra 177 (1995), 926–960. Google Scholar

[KS] [KS] Kearnes, K., Szendrei, A., The Relationship Between Two Commutators. Internat. J. Algebra Comput. (to appear). Google Scholar

[Lp1] [Lp1] Lipparini, P., A characterization of varieties with a difference term. Canad. Math. Bull. (3) 39 (1996), 308–315. Google Scholar

[Lp2] [Lp2] Lipparini, P., Difference terms and commutators. Manuscript. Google Scholar

[Lp3] [Lp3] Lipparini, P., n-permutable varieties satisfy non trivial congruence identities. Algebra Universalis 33 (1995), 159–168. Google Scholar

[Lp4] [Lp4] Lipparini, P., Commutator Theory without join-distributivity. Trans. Amer.Math. Soc. 346 (1994), 177–202. Google Scholar

[MKNT] [MKNT] McKenzie, R., McNulty, G. and Taylor, W., Algebras, Lattices, Varieties. Wadsworth & Brooks/Cole Mathematics Series 1, Monterey, 1987. Google Scholar

[Qu] [Qu] Quackenbush, R., Quasi-affine algebras. Algebra Universalis 20 (1985), 318–327. Google Scholar

[Ta] [Ta] Taylor, W., Characterizing Mal’cev conditions. Algebra Universalis 3 (1973), 351–397. Google Scholar

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