An example of a limit variety of semigroups

1982 ◽  
Vol 24 (1) ◽  
pp. 319-326 ◽  
Author(s):  
M. V. Volkov
Keyword(s):  
Variety Of Semigroups ◽  
Limit Variety

Undecidability of the identity problem for finite semigroups

1992 ◽  
Vol 57 (1) ◽  
pp. 179-192 ◽  
Author(s):  
Douglas Albert ◽  
Robert Baldinger ◽  
John Rhodes
Keyword(s):  
Word Problem ◽  
Finite Semigroup ◽  
Identity Problem ◽  
Finite Semigroups ◽  
Or Groups ◽  
Finite Set ◽  
Variety Of Semigroups ◽  
Finite Products

In 1947 E. Post [28] and A. A. Markov [18] independently proved the undecidability of the word problem (or the problem of deducibility of relations) for semigroups. In 1968 V. L. Murskil [23] proved the undecidability of the identity problem (or the problem of deducibility of identities) in semigroups.If we slightly generalize the statement of these results we can state many related results in the literature and state our new results proved here. Let V denote either a (Birkhoff) variety of semigroups or groups or a pseudovariety of finite semigroups. By a very well-known theorem a (Birkhoff) variety is defined by equations or equivalently closed under substructure, surmorphisms and all products; see [7]. It is also well known that V is a pseudovariety of finite semigroups iff V is closed under substructure, surmorphism and finite products, or, equivalently, determined eventually by equations w1 = w1′, w2 = w2′, w3 = w3′,… (where the finite semigroup S eventually satisfies these equations iff there exists an n, depending on S, such that S satisfies Wj = Wj′ for j ≥ n). See [8] and [29]. All semigroups form a variety while all finite semigroups form a pseudovariety.We now consider a table (see the next page). In it, for example, the box denoting the “word” (identity) problem for the psuedovariety V” means, given a finite set of relations (identities) E and a relation (identity) u = ν, the problem of whether it is decidable that E implies u = ν inside V.

Artin theorem for semigroups

2017 ◽  
Vol 16 (02) ◽  
pp. 1750034
Author(s):  
T. A. Hakobyan ◽  
Yu. M. Movsisyan
Keyword(s):  
Type Theorem ◽  
Variety Of Semigroups

In this paper, we prove an Artin type theorem for semigroups. Namely, we consider the concepts of hyperalternative and hyperassociative semigroups and prove that every two elements in any hyperalternative semigroup generate a hyperassociative subsemigroup. As a consequence, we characterize all hyperalternative semigroups, and prove that these semigroups form a variety of semigroups with four identities.

INTERPRETING GRAPH COLORABILITY IN FINITE SEMIGROUPS

2006 ◽  
Vol 16 (01) ◽  
pp. 119-140 ◽  
Author(s):  
MARCEL JACKSON ◽  
RALPH McKENZIE
Keyword(s):  
Membership Problem ◽  
Finite Semigroups ◽  
Variety Of Semigroups ◽  
Membership Problems

We show that a number of natural membership problems for classes associated with finite semigroups are computationally difficult. In particular, we construct a 55-element semigroup S such that the finite membership problem for the variety of semigroups generated by S interprets the graph 3-colorability problem.

The ascending varietal chain of a variety of semigroups

1986 ◽  
Vol 35 (1) ◽  
pp. 157-162 ◽  
Author(s):  
A. N. Petrov
Keyword(s):  
Variety Of Semigroups

A new example of limit variety

1989 ◽  
Vol 38 (1) ◽  
pp. 283-303 ◽  
Author(s):  
György Pollák
Keyword(s):  
Limit Variety

A variety of semigroups without an irreducible basis for identities

1977 ◽  
Vol 21 (6) ◽  
pp. 487-490
Author(s):  
A. N. Trakhtman
Keyword(s):  
Variety Of Semigroups

All subvarieties of a certain variety of semigroups

1974 ◽  
Vol 7 (1-4) ◽  
pp. 104-152 ◽  
Author(s):  
Mario Petrich
Keyword(s):  
Variety Of Semigroups

FINITELY GENERATED LIMIT VARIETIES OF APERIODIC MONOIDS WITH CENTRAL IDEMPOTENTS

2009 ◽  
Vol 08 (06) ◽  
pp. 779-796 ◽  
Author(s):  
EDMOND W. H. LEE
Keyword(s):  
Present Article ◽  
Variety Of Algebras ◽  
Finitely Based ◽  
Finitely Generated ◽  
Finitely Based Variety ◽  
Limit Variety ◽  
Aperiodic Monoids

A non-finitely based variety of algebras is said to be a limit variety if all its proper subvarieties are finitely based. Recently, Marcel Jackson published two examples of finitely generated limit varieties of aperiodic monoids with central idempotents and questioned whether or not they are unique. The present article answers this question affirmatively.

scholarly journals Green's-Like Relations on Algebras and Varieties

2008 ◽  
Vol 2008 ◽  
pp. 1-12
Author(s):  
K. Denecke ◽  
S. L. Wismath
Keyword(s):  
Binary Operation ◽  
Equivalence Relations ◽  
Green’S Relations ◽  
Green's Relations ◽  
Variety Of Semigroups

There are five equivalence relations known as Green's relations definable on any semigroup or monoid, that is, on any algebra with a binary operation which is associative. In this paper, we examine whether Green's relations can be defined on algebras of any typeτ. Some sort of (super-)associativity is needed for such definitions to work, and we consider algebras which are clones of terms of typeτ, where the clone axioms including superassociativity hold. This allows us to define for any varietyVof typeτtwo Green's-like relationsℒVandℛVon the term clone of typeτ. We prove a number of properties of these two relations, and describe their behaviour whenVis a variety of semigroups.

A SUFFICIENT CONDITION UNDER WHICH A SEMIGROUP IS NONFINITELY BASED

2015 ◽  
Vol 93 (3) ◽  
pp. 454-466
Author(s):  
WEN TING ZHANG ◽  
YAN FENG LUO
Keyword(s):  
Forthcoming Paper ◽  
Additional Analysis ◽  
Sufficient Condition ◽  
Limit Variety ◽  
Aperiodic Monoids ◽  
Nonfinitely Based

We give a sufficient condition under which a semigroup is nonfinitely based. As an application, we show that a certain variety is nonfinitely based, and we indicate the additional analysis (to be presented in a forthcoming paper), which shows that this example is a new limit variety of aperiodic monoids.

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