Vol. 5, No. 3, 2012

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$k$-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
Mathematical Subject Classification 2010
Primary: 11Y05
Milestones
Received: 23 June 2011
Revised: 7 February 2012
Accepted: 9 February 2012
Published: 14 April 2013

Communicated by Scott Chapman
Authors
Nicholas R. Baeth
Department of Mathematics and Computer Science
University of Central Missouri
Warrensburg, MO 64093
United States
Kaitlyn Cassity
Department of Mathematics and Computer Science
University of Central Missouri
Warrensburg, MO 64093
United States