#### Vol. 5, No. 3, 2012

 Recent Issues
 The Journal Cover Page Editorial Board Editors’ Addresses Editors’ Interests About the Journal Scientific Advantages Submission Guidelines Submission Form Ethics Statement Subscriptions Editorial Login Author Index Coming Soon Contacts ISSN: 1944-4184 (e-only) ISSN: 1944-4176 (print)
$k$-furcus semigroups

### Nicholas R. Baeth and Kaitlyn Cassity

Vol. 5 (2012), No. 3, 295–302
##### Abstract

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.

##### Keywords
semigroups, factorization
Primary: 11Y05