Article

Lamron -groups

Published in: Quaestiones Mathematicae
Volume 41, issue 1, 2018 , pages: 81–98
DOI: 10.2989/16073606.2017.1372529
Author(s): Papiya BhattacharjeePenn State Behrend, School of Science,, Warren Wm. McGovernH.L. Wilkes Honors College,

Abstract

The article introduces a new class of lattice-ordered groups. An -group G is lamron if Min(G)−1 is a Hausdorff topological space, where Min(G)−1 is the space of all minimal prime subgroups of G endowed with the inverse topology. It will be evident that lamron -groups are related to -groups with stranded primes. In particular, it is shown that for a W-object (G,u), if every value of u contains a unique minimal prime subgroup, then G is a lamron -group; such a W-object will be said to have W-stranded primes. A diverse set of examples will be provided in order to distinguish between the notions of lamron, stranded primes, W-stranded primes, complemented, and weakly complemented -groups.

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