The notion of a weakly associative lattice group is a generalization of that of a lattice ordered group in which the identities of associativity of the lattice operations join and meet are replaced by the identities of weak associativity. In the paper, the spectral topologies on the sets of straightening ideals (and on some of their subsets) of abelian weakly associative lattice groups are intr...

The focus of this paper is the class of perfect GMV-algebras, which includes all non-commutative analogues of perfect MV-algebras. As in the commutative case, we show that each perfect GMV-algebra possesses a single negation, it is generated by its infinitesimal elements, and can be realized as an interval in a lexicographical product of the lattice-ordered group of integers and an arbitrary la...

Example 1. Let G be a finite group. Then the set of all subgroups of G, partially ordered by inclusion, is a lattice. For H ≤ G the sublattice OG(H) of overgroups of H in G is the interval sublattice [H,G]. Call such a lattice a finite group interval lattice. There is a well-known open question as to whether every nonempty finite lattice is isomorphic to a finite group interval lattice. See [PP...