WELL- AND BETTER-QUASI-ORDERINGS IN THE LATTICE OF VARIETIES OF COMMUTATIVE SEMIGROUPS
Mariusz Grech · International Journal of Algebra and Computation · 2007
In this paper, we describe all subsets of the lattices [Formula: see text] and [Formula: see text] of varieties (and pseudovarieties) of commutative semigroups which have the property of being a better-quasi-ordering (well-quasi-ordering). In particular, we show that the lattice [Formula: see text] of varieties of commutative nilpotent semigroups is a better-quasi-ordering, which solves a problem posed by Almeida.1.