Abstract
It is usual in Mathematics to represent objects by means of a free object modulo certain relations fulfilled by the generators of the free object. The reader familiar to group theory surely has used many times definitions of groups by means of generators and relations. Relations are usually represented as equalities, or simply words in the free group on the generators (this means that they are equal to the identity element; this is due to the fact that we have inverse in groups). Here we represent relations by pairs. These are pairs of factorizations of certain elements in the semigroup; they will be a crucial tool for studying factorizations in the next chapter.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Assi, A., García-Sánchez, P.A. (2016). Minimal Presentations. In: Numerical Semigroups and Applications. RSME Springer Series, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-41330-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-41330-3_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-41329-7
Online ISBN: 978-3-319-41330-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)