k-furcus semigroups

Baeth, Nicholas; Cassity, Kaitlyn

doi:10.2140/involve.2012.5.295

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$k$-furcus semigroups

Nicholas R. Baeth and Kaitlyn Cassity

Vol. 5 (2012), No. 3, 295–302

DOI: 10.2140/involve.2012.5.295

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

Vol. 5, No. 3, 2012