A four-element algebra whose identities are not finitely based

1980 ◽  
Vol 11 (1) ◽  
pp. 255-260 ◽  
Author(s):  
Robert E. Park
Keyword(s):  
Finitely Based

FINITELY BASED WORDS

2000 ◽  
Vol 10 (04) ◽  
pp. 457-480 ◽  
Author(s):  
OLGA SAPIR
Keyword(s):  
Sufficient Conditions ◽  
Basis Property ◽  
Free Monoid ◽  
Finite Basis ◽  
Finitely Based ◽  
Finite Basis Property ◽  
Letter Alphabet ◽  
Finite Language ◽  
Rees Quotient ◽  
The Ideal

Let W be a finite language and let Wc be the closure of W under taking subwords. Let S(W) denote the Rees quotient of a free monoid over the ideal consisting of all words that are not in Wc. We call W finitely based if the monoid S(W) is finitely based. Although these semigroups have easy structure they behave "generically" with respect to the finite basis property [6]. In this paper, we describe all finitely based words in a two-letter alphabet. We also find some necessary and some sufficient conditions for a set of words to be finitely based.

A JUST NON-FINITELY BASED VARIETY OF BIGROUPS

2001 ◽  
Vol 29 (9) ◽  
pp. 4011-4046 ◽  
Author(s):  
C. K. Gupta* ◽  
A. N. Krasilnikov
Keyword(s):  
Finitely Based ◽  
Finitely Based Variety

scholarly journals POSITIVE FRAGMENTS OF RELEVANCE LOGIC AND ALGEBRAS OF BINARY RELATIONS

2010 ◽  
Vol 4 (1) ◽  
pp. 81-105 ◽  
Author(s):  
ROBIN HIRSCH ◽  
SZABOLCS MIKULÁS
Keyword(s):  
Equational Theory ◽  
Relevance Logic ◽  
Binary Relations ◽  
Finitely Based ◽  
Similarity Type ◽  
Relation Composition

We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a nonfinitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.

A SIMPLE EXAMPLE OF A NON-FINITELY BASED SYSTEM OF POLYNOMIAL IDENTITIES

2002 ◽  
Vol 30 (10) ◽  
pp. 4851-4866 ◽  
Author(s):  
C. K. Gupta ◽  
Alexei N. Krasilnikov
Keyword(s):  
Finitely Based ◽  
Polynomial Identities

scholarly journals A proof of Zhil'tsov's theorem on decidability of equational theory of epigroups

2016 ◽  
Vol Vol. 17 no. 3 (Combinatorics) ◽  
Author(s):  
Inna Mikhaylova
Keyword(s):  
Finite Semigroup ◽  
Equational Theory ◽  
Unary Operation ◽  
Finitely Based ◽  
Infinite Basis ◽  
International Audience

International audience Epigroups are semigroups equipped with an additional unary operation called pseudoinversion. Each finite semigroup can be considered as an epigroup. We prove the following theorem announced by Zhil'tsov in 2000: the equational theory of the class of all epigroups coincides with the equational theory of the class of all finite epigroups and is decidable. We show that the theory is not finitely based but provide a transparent infinite basis for it.

scholarly journals Bisimilarity is not Finitely Based over BPA with Interrupt

2005 ◽  
Vol 12 (33) ◽  
Author(s):  
Luca Aceto ◽  
Willem Jan Fokkink ◽  
Anna Ingólfsdóttir ◽  
Sumit Nain
Keyword(s):  
Process Algebra ◽  
Sharp Contrast ◽  
Basic Process ◽  
Finitely Based ◽  
Bisimulation Equivalence

This paper shows that bisimulation equivalence does not afford a finite equational axiomatization over the language obtained by enriching Bergstra and Klop's Basic Process Algebra with the interrupt operator. Moreover, it is shown that the collection of closed equations over this language is also not finitely based. In sharp contrast to these results, the collection of closed equations over the language BPA enriched with the disrupt operator is proven to be finitely based.

scholarly journals On some varieties of ai-semirings satisfying xp+1 ≈ x

2018 ◽  
Vol 16 (1) ◽  
pp. 913-923
Author(s):  
Aifa Wang ◽  
Yong Shao
Keyword(s):  
Distributive Lattice ◽  
Finitely Based ◽  
Finitely Generated ◽  
Lattice Of Subvarieties

AbstractThe aim of this paper is to study the lattice of subvarieties of the ai-semiring variety defined by the additional identities$$\begin{array}{} \displaystyle x^{p+1}\approx x\,\,\mbox{and}\,\,zxyz\approx(zxzyz)^{p}zyxz(zxzyz)^{p}, \end{array} $$wherepis a prime. It is shown that this lattice is a distributive lattice of order 179. Also, each member of this lattice is finitely based and finitely generated.

A non-finitely-based variety of center-by-metabelian pointed groups

2014 ◽  
Vol 95 (5-6) ◽  
pp. 743-746
Author(s):  
G. S. Deryabina ◽  
A. N. Krasil’nikov
Keyword(s):  
Finitely Based ◽  
Finitely Based Variety
Sign in / Sign up

Export Citation Format

Share Document