Inherently nonfinitely based finite algebras

1983 ◽  
pp. 206-231 ◽  
Author(s):  
George F. McNulty ◽  
Caroline R. Shallon
Keyword(s):  
Finite Algebras ◽  
Nonfinitely Based

scholarly journals EQUATIONAL COMPLEXITY OF THE FINITE ALGEBRA MEMBERSHIP PROBLEM

2008 ◽  
Vol 18 (08) ◽  
pp. 1283-1319 ◽  
Author(s):  
GEORGE F. McNULTY ◽  
ZOLTÁN SZÉKELY ◽  
ROSS WILLARD
Keyword(s):  
Finite Automata ◽  
Finite Algebra ◽  
Equational Theory ◽  
Upper And Lower Bounds ◽  
Variety Of Algebras ◽  
Membership Problem ◽  
Finite Algebras ◽  
Shift Automorphism ◽  
Positive Integers ◽  
Nonfinitely Based

We associate to each variety of algebras of finite signature a function on the positive integers called the equational complexity of the variety. This function is a measure of how much of the equational theory of a variety must be tested to determine whether a finite algebra belongs to the variety. We provide general methods for giving upper and lower bounds on the growth of equational complexity functions and provide examples using algebras created from graphs and from finite automata. We also show that finite algebras which are inherently nonfinitely based via the shift automorphism method cannot be used to settle an old problem of Eilenberg and Schützenberger.

scholarly journals A minimal nonfinitely based semigroup whose variety is polynomially recognizable

2011 ◽  
Vol 177 (6) ◽  
pp. 847-859 ◽  
Author(s):  
M. V. Volkov ◽  
S. V. Goldberg ◽  
S. I. Kublanovsky
Keyword(s):  
Nonfinitely Based

scholarly journals On representing Mn's by congruence lattice of finite algebras

1983 ◽  
Vol 44 (3) ◽  
pp. 299-308 ◽  
Author(s):  
M.G. Stone ◽  
R.H. Weedmark
Keyword(s):  
Congruence Lattice ◽  
Finite Algebras

On Pseudovarieties of Forest Algebras

2016 ◽  
Vol 27 (08) ◽  
pp. 909-941 ◽  
Author(s):  
Saeid Alirezazadeh
Keyword(s):  
Natural Extension ◽  
Direct Products ◽  
Property A ◽  
Residually Finite ◽  
Finite Algebras

Forest algebras are defined for investigating languages of forests [ordered sequences] of unranked trees, where a node may have more than two [ordered] successors. They consist of two monoids, the horizontal and the vertical, with an action of the vertical monoid on the horizontal monoid, and a complementary axiom of faithfulness. In the study of forest algebras one of the main difficulties is how to handle the faithfulness property. A pseudovariety is a class of finite algebras of a given signature, closed under the taking of homomorphic images, subalgebras and finitary direct products. We tried to adapt in this context some of the results in the theory of semigroups, specially the studies on relatively free profinite semigroups, which are an important tool in the theory of pseudovarieties of semigroups. We define a new version of syntactic congruence of a subset of the free forest algebra, not just a forest language. This new version is the natural extension of the syntactic congruence for monoids in the case of forest algebras and is used in the proof of an analog of Hunter’s Lemma. We show that under a certain assumption the two versions of syntactic congruences coincide. We adapt some results of Almeida on metric semigroups to the context of forest algebras. We show that the analog of Hunter’s Lemma holds for metric forest algebras, which leads to the result that zero-dimensional compact metric forest algebras are residually finite. We show an analog of Reiterman’s Theorem, which is based on a study of the structure profinite forest algebras.

scholarly journals DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS

2014 ◽  
Vol 57 (3) ◽  
pp. 693-707
Author(s):  
YEMON CHOI
Keyword(s):  
Invertible Element ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Complex Line ◽  
Locally Compact ◽  
The Real ◽  
C Algebra ◽  
Finite Algebras ◽  
Unimodular Group ◽  
Reduced Group

AbstractAn algebraAis said to be directly finite if each left-invertible element in the (conditional) unitization ofAis right invertible. We show that the reduced group C*-algebra of a unimodular group is directly finite, extending known results for the discrete case. We also investigate the corresponding problem for algebras ofp-pseudofunctions, showing that these algebras are directly finite ifGis amenable and unimodular, or unimodular with the Kunze–Stein property. An exposition is also given of how existing results from the literature imply thatL1(G) is not directly finite whenGis the affine group of either the real or complex line.

scholarly journals Finite algebras of finite complexity

1999 ◽  
Vol 207 (1-3) ◽  
pp. 89-135 ◽  
Author(s):  
Keith A. Kearnes ◽  
Emil W. Kiss
Keyword(s):  
Finite Algebras

scholarly journals A characterization of representation-finite algebras

1991 ◽  
Vol 140 (1) ◽  
pp. 31-34
Author(s):  
Andrzej Skowroński ◽  
M. Wenderlich
Keyword(s):  
Finite Algebras

A factorization procedure for finite algebras

1982 ◽  
Vol 25 (1) ◽  
pp. 51-81 ◽  
Author(s):  
Philippa E Pattison ◽  
Warren K Bartlett
Keyword(s):  
Finite Algebras
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