We study splittings or lack of them, in lattices of subvarieties of some logic-related varieties. We present a general lemma, the non-splitting lemma, which when combined with some variety-specific constructions, yields each of our negative results: the variety of commutative integral residuated lattices contains no splitting algebras, and in the varieties of double Heyting algebras, dually pseudocomplemented Heyting algebras and regular double p-algebras the only splitting algebras are the two-element and three-element chains.

中文翻译：

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各种逻辑的分裂

我们在一些与逻辑相关的品种的子品种的格子中研究分裂或缺乏分裂。我们提出了一个一般引理，即非分裂引理，当它与一些特定于簇的构造结合时，会产生我们的每一个否定结果：交换积分剩余格的多样性不包含分裂代数，并且在双 Heyting 代数的变体中，对偶伪补 Heyting 代数和正则双p-algebras 唯一的分裂代数是二元链和三元链。