Lexico groups and direct products of lattice ordered groups

Year, pages: 2016, 35 - 42

A lattice ordered group $A$ will be said to be a lexico group if there exists a convex $\ell$-subgroup $A₀$ of $A$ with $A₀≠ A$ such that for each $a\in A\setminus A₀$ we have either $a > a₀$ for each $a₀\in A₀$, or $a0$ for each $a₀\in A₀$. We prove the following result. Let $A$ be a convex $\ell$-subgroup of a lattice ordered group $G$ such that (i) $A$ is a lexico group, and (ii) $A$ fails to be upper bounded in $G$. Then $A$ is a direct factor of $G$.

Jakubík, J. 2016. Lexico groups and direct products of lattice ordered groups. In Mathematica Slovaca, vol. 66, no.1, pp. 35-42. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0113

Jakubík, J. (2016). Lexico groups and direct products of lattice ordered groups. Mathematica Slovaca, 66(1), 35-42. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0113