无有限性的立方项阻塞器
Cube term blockers without finiteness
摘要：
证明了一个幂等簇有$d$维立方项当且仅当它在两个生成元上的自由代数没有$d$维相容交叉.本文利用Hall婚姻定理证明了基本运算为$n_1, \ldots, n_k$的有限签名有$d$维立方项的充要条件是它有一个$d=1+\sum_{i=1}^k (n_i-1)$维.这个下界的尺寸是尖锐的。证明了纯循环项簇有立方项当且仅当它不含$2$ -元半格。证明了在幂等Maltsev条件格中，Maltsev条件“立方项存在”是并素的。
英文摘要：
We show that an idempotent variety has a $d$-dimensional cube term if and only if its free algebra on two generators has no $d$-ary compatible cross. We employ Hall's Marriage Theorem to show that a variety of finite signature whose fundamental operations have arities $n_1, \ldots, n_k$ has a $d$-dimensional cube term if and only if it has one of dimension $d=1+\sum_{i=1}^k (n_i-1)$. This lower bound on dimension is shown to be sharp. We show that a pure cyclic term variety has a cube term if and only if it contains no $2$-element semilattice. We prove that the Maltsev condition "existence of a cube term" is join prime in the lattice of idempotent Maltsev conditions.
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