k-furcus semigroups
Nicholas R. Baeth, Kaitlyn Cassity · Involve a Journal of Mathematics · 2012
A bifurcus semigroup is a semigroup in which every nonunit nonatom can be written as the product of exactly two atoms.We generalize this notion to k-furcus semigroups: every element that can be factored as the product of at least k nonunits can be factored as the product of exactly k atoms.We compute some factorization-theoretic invariants of k-furcus semigroups that generalize the bifurcus results.We then define two variations on the k-furcus property, one stronger (presumabaly strictly) and the other strictly weaker than the k-furcus property.