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.
 I. Chajda and R. Halaš: Congruence modularity at 0
. Discuss. Math., Algebra and Stochast. Methods 17 (1997), 57–65. MR 1633236