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regularity; modularity; semiregularity; modularity at 0
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.
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[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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