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Fundam. Prikl. Mat., 2019, Volume 22, Issue 4, Pages 239–252 (Mi fpm1827)  

On convex directed subgroups of pseudo lattice-ordered groups

E. E. Shirshova

Moscow State Pedagogical University

Abstract: We show that all convex directed subgroups of a $pl$-group form a distributive lattice under inclusions that is a Brouwer lattice. We succeeded in extending some $l$-group results concerning rectifying and regular subgroups to the class of $\mathcal{AO}$-groups. Necessary and sufficient conditions are given for an element of a $pl$-group to be an element with a unique value. In order to prove this, some properties of lexicographic extensions of $\mathcal{AO}$-groups and $pl$-groups are investigated.

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UDC: 512.545

Citation: E. E. Shirshova, “On convex directed subgroups of pseudo lattice-ordered groups”, Fundam. Prikl. Mat., 22:4 (2019), 239–252

Citation in format AMSBIB
\Bibitem{Shi19}
\by E.~E.~Shirshova
\paper On convex directed subgroups of pseudo lattice-ordered groups
\jour Fundam. Prikl. Mat.
\yr 2019
\vol 22
\issue 4
\pages 239--252
\mathnet{http://mi.mathnet.ru/fpm1827}


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  • Фундаментальная и прикладная математика
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