Lamron ℓ-groups

Abstract

The article introduces a new class of lattice-ordered groups. An ℓ-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 ℓ-groups are related to ℓ-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 ℓ-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 ℓ-groups.

Mathematics Subject Classification (2010):

• Primary: 06F15
• Secondary: 06F20
• 54G

Key words:

• Lattice-ordered group
• minimal prime subgroups
• stranded primes
• archimedean ℓ-group
• W