Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Congruences associated with DOL-schemes

Authors: Mario Petrich and Gabriel Thierrin
Journal: Proc. Amer. Math. Soc. 102 (1988), 787-793
MSC: Primary 68Q45; Secondary 20M05, 20M35
MathSciNet review: 934843
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For a DOL-scheme $ (X,\varphi )$, where $ X$ is a finite alphabet and $ \varphi $ is an endomorphism of $ {X^*}$, we study the properties of the congruence $ \bar \varphi $ induced by $ \varphi $ in terms of the properties of $ {X^*}\varphi $. We prove that every submonoid of $ {X^*}$ has a disjunctive subset (for any $ X$) and deduce that $ \bar \varphi $ is a syntactic congruence. As special cases, we consider the conditions on $ \varphi $ which are equivalent to $ \bar \varphi $ being perfect or uniquely perfect or linear. The latter is introduced in the paper together with a ramification.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 68Q45, 20M05, 20M35

Retrieve articles in all journals with MSC: 68Q45, 20M05, 20M35

Additional Information

PII: S 0002-9939(1988)0934843-7
Keywords: Free monoid, endomorphism, DOL-scheme, syntactic congruence, perfect congruence, linear congruence, code, hypercode
Article copyright: © Copyright 1988 American Mathematical Society