原始晶格变体

P. Jipsen, J. B. Nation
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引用次数: 2

摘要

如果每一个拟变量都是相等的,则一个变量是原始的,即一个子变量。在本文中,我们探讨了原始晶格变分与惠特曼条件之间的联系[公式:见正文]。例如,如果局部有限变[公式:见文]中的每一个有限子直接不可约格都满足惠特曼条件[公式:见文],则[公式:见文]是本原格。这允许我们构造无限多的原始格变体序列,并证明存在这样的变体[公式:见文本]。一些失败的格(公式:见文本)也会生成原始变体。但如果[公式:见文]是有限子直接不可约格[公式:见文]中的[公式:见文]失效区间,且[公式:见文]表示[公式:见文]加倍的格,则[公式:见文]绝不是原元。
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Primitive lattice varieties
A variety is primitive if every subquasivariety is equational, i.e. a subvariety. In this paper, we explore the connection between primitive lattice varieties and Whitman’s condition [Formula: see text]. For example, if every finite subdirectly irreducible lattice in a locally finite variety [Formula: see text] satisfies Whitman’s condition [Formula: see text], then [Formula: see text] is primitive. This allows us to construct infinitely many sequences of primitive lattice varieties, and to show that there are [Formula: see text] such varieties. Some lattices that fail [Formula: see text] also generate primitive varieties. But if [Formula: see text] is a [Formula: see text]-failure interval in a finite subdirectly irreducible lattice [Formula: see text], and [Formula: see text] denotes the lattice with [Formula: see text] doubled, then [Formula: see text] is never primitive.
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