Amalgamation bases for the class of lattice-ordered groups

作者：Bludov V V^*; Glass A M W

来源：Mathematica Slovaca, 2014, 64(3): 571-578.

DOI：10.2478/s12175-014-0227-5

• amalgamation
• lattice-ordered group
• l-permutation group

We prove
Theorem A. The cardinal product of two copies of the integers is an amalgamation base for the class of all lattice-ordered groups but their lexicographic product is not.
This answers Problem 27 of [Black Swamp Problem Book (W. Charles Holland, ed.), Bowling Green State University, 1982].
Theorem B. he cardinal product of n copies of the integers is not an amalgamation base for the class of all lattice-ordered groups if n >= 3.

• 出版日期2014-6