代数簇对的临界点
Critical points of pairs of varieties of algebras
摘要：
对于代数类V，用Conc（V）表示同构于A的所有紧同余的半格Conc（A）的所有半格的类。对于代数类V1和V2，我们用crit（V1，V2）表示Conc（V1）中的一个半格的最小基数，如果它存在，它不在Conc（V2）中，否则为无穷大。本文证明了一个具有范畴性质的一般定理，它意味着对于所有的非线性生成的同余分配簇V1和V2，crit（V1，V2）要么是有限的，要么是对某个自然数n的aleph_n，要么是无穷大的.我们还找到了两个可生成的模格簇V1和V2，使得crit（V1，V2）=aleph_1，从而回答了J.Tuma和F.威龙
英文摘要：
For a class V of algebras, denote by Conc(V) the class of all semilattices isomorphic to the semilattice Conc(A) of all compact congruences of A, for some A in V. For classes V1 and V2 of algebras, we denote by crit(V1,V2) the smallest cardinality of a semilattice in Conc(V1) which is not in Conc(V2) if it exists, infinity otherwise. We prove a general theorem, with categorical flavor, that implies that for all finitely generated congruence-distributive varieties V1 and V2, crit(V1,V2) is either finite, or aleph_n for some natural number n, or infinity. We also find two finitely generated modular lattice varieties V1 and V2 such that crit(V1,V2)=aleph_1, thus answering a question by J. Tuma and F. Wehrung.
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