The amalgamation property in equational classes of modular lattices.
The amalgamation property in equational classes of modular lattices.
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模格方程类中的并合性质。
DOI：
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发表时间：
1973
期刊：
影响因子：
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通讯作者：
H. Lakser
中科院分区：
文献类型：
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作者：
G. Grätzer;B. Jónsson;H. Lakser
关于合并财产的历史和重要性，我们建议读者参考 B. Jonsson [8]（另请参阅 G. Gratzer [5]）。所有格的类和所有分配格的类都具有合并·性质。所有模格子的M类是否具有合并性质的问题已经存在了十多年。 1971 年 1 月，B. Jonsson 宣布 [11] M 不具有合并性质，事实上，任何具有合并性质的模格的方程类 K 都必须满足争论恒等式。随后 G. Gratzer 和 H. Lakser [7] 宣布 K 的每个成员都可以嵌入到无限维射影几何的子空间晶格中。结合并扩展这些结果，我们现在可以证明以下内容：
For the history and importance of the Amalgamation Property we refer the reader to B. Jonsson [8] (see also G. Gratzer [5]). The class of all lattices and the class of all distributive lattices both have the Amalgamation ·Property. The problem whether the class M of all modular lattices has the Amalgamation Property has been around for more than a decade. In January of 1971 B. Jonsson announced [11] that M does not have the Amalgamation Property, in fact, any equational class K of modular lattices having the Amalgamation Property must satisfy the arguesian identity. This was followed by an announcement by G. Gratzer and H. Lakser [7] stating that every member of K can be embedded into the subspace lattice of an infinite dimensional projective geometry. Combining and extending these results, we can now prove the following: