Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The syntactic monoid of the semigroup
generated by a maximal prefix code


Authors: Mario Petrich, C. M. Reis and G. Thierrin
Journal: Proc. Amer. Math. Soc. 124 (1996), 655-663
MSC (1991): Primary 20M35
MathSciNet review: 1317045
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we investigate the semigroup structure of the syntactic monoid $\mathrm {Syn}(C^+)$ of $C^+$, the semigroup generated by a maximal prefix code $C$ for which $C^+$ is a single class of the syntactic congruence. In particular we prove that for such a prefix code $C$, either $\mathrm {Syn}(C^+)$ is a group or it is isomorphic to a special type of submonoid of $G\times \mathcal{T}(R)$ where $G$ is a group and $\mathcal {T}(R)$ is the full transformation semigroup on a set $R$ with more than one element. From this description we conclude that $\mathrm {Syn}(C^+)$ has a kernel $J$ which is a right group. We further investigate separately the case when $J$ is a right zero semigroup and the case when $J$ is a group.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20M35

Retrieve articles in all journals with MSC (1991): 20M35


Additional Information

Mario Petrich
Affiliation: The University of Western Ontario, London, Ontario, Canada N6A 5B7

C. M. Reis
Affiliation: The University of Western Ontario, London, Ontario, Canada N6A 5B7

G. Thierrin
Affiliation: The University of Western Ontario, London, Ontario, Canada N6A 5B7

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03271-6
PII: S 0002-9939(96)03271-6
Keywords: Free semigroups, syntactic monoid, maximal prefix code
Received by editor(s): September 23, 1993
Additional Notes: This work was supported by the Natural Sciences and Engineering Research Council of Canada, Grants S174A3 and S078A1
Communicated by: Lance W. Small
Article copyright: © Copyright 1996 American Mathematical Society