TY - JOUR
T1 - Comparing Semigroup and Monoid Presentations for Finite Monoids
AU - Campbell, Colin Matthew
AU - Mitchell, James David
AU - Ruskuc, Nikola
N1 - Mitchell was a Ph.D. student of Ruskuc and Campbell
PY - 2002/2
Y1 - 2002/2
N2 - It is known that for any finite group G given by a finite group presentation (A\R) there exists a finite semigroup presentation for G of the same deficiency, i.e. satisfying \Q\ - \B\ = \R\ - \A\. It is also known that the analogous statement does not hold for all finite monoids. In this paper we give a necessary and sufficient condition for a finite monoid M, given by a finite monoid presentation, to have a finite semigroup presentation of the same deficiency.
AB - It is known that for any finite group G given by a finite group presentation (A\R) there exists a finite semigroup presentation for G of the same deficiency, i.e. satisfying \Q\ - \B\ = \R\ - \A\. It is also known that the analogous statement does not hold for all finite monoids. In this paper we give a necessary and sufficient condition for a finite monoid M, given by a finite monoid presentation, to have a finite semigroup presentation of the same deficiency.
KW - semigroup presentations
KW - monoid presentations
KW - deficiency
UR - http://www.scopus.com/inward/record.url?scp=20344393620&partnerID=8YFLogxK
U2 - 10.1007/s605-002-8263-7
DO - 10.1007/s605-002-8263-7
M3 - Article
SN - 1436-5081
VL - 134
SP - 287
EP - 293
JO - Monatshefte für Mathematik
JF - Monatshefte für Mathematik
IS - 4
ER -