Please use this identifier to cite or link to this item:
https://open.uns.ac.rs/handle/123456789/25416
Title: | The variety of Kleene algebras with conversion is not finitely based | Authors: | Crvenković Siniša Dolinka Igor Ésik Zoltan |
Issue Date: | 2000 | Journal: | Theoretical Computer Science | Abstract: | Given an arbitrary set A, one obtains the full Kleene algebra of binary relations over A by considering the operations of union, composition, reflexive-transitive closure, conversion, and the empty set and the identity relation as constants. Such algebras generate the variety of Kleene algebras (with conversion). As a result of a general analysis of identities satisfied by varieties having an involution operation, we prove that the variety of Kleene algebras with conversion has no finite equational axiomatization. In our argument we make use of the fact that the variety of Kleene algebras without conversion is not finitely based and that, relatively to this variety, the variety of Kleene algebras with conversion is finitely axiomatized. © 2000 Elsevier Science B.V. All rights reserved. | URI: | https://open.uns.ac.rs/handle/123456789/25416 | ISSN: | 0304-3975 | DOI: | 10.1016/S0304-3975(99)00079-1 |
Appears in Collections: | PMF Publikacije/Publications |
Show full item record
SCOPUSTM
Citations
22
checked on Nov 20, 2023
Page view(s)
7
Last Week
1
1
Last month
0
0
checked on May 10, 2024
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.