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Article

Chajda, Ivan
Semiregularity of congruences implies congruence modularity at 0. (English). Czechoslovak Mathematical Journal, vol. 52 (2002), issue 2, pp. 333-336
MSC: 08A30, 08B10 | MR 1905440 | Zbl 1011.08002
Keywords:
regularity; modularity; semiregularity; modularity at 0
Summary:
We introduce a weakened form of regularity, the so called semiregularity, and we show that if every diagonal subalgebra of $\mathcal A \times \mathcal A$ is semiregular then $\mathcal A$ is congruence modular at 0.
References:
[1] S. Bulman-Fleming, A. Day and W. Taylor: Regularity and modularity of congruences. Algebra Universalis 4 (1974), 58–60. DOI 10.1007/BF02485707 | MR 0382118
[2] I. Chajda: Locally regular varieties. Acta Sci. Math. (Szeged) 64 (1998), 431–435. MR 1666006 | Zbl 0913.08006
[3] I. Chajda and R. Halaš: Congruence modularity at 0. Discuss. Math., Algebra and Stochast. Methods 17 (1997), 57–65. MR 1633236
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