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Slim groupoids

Jaroslav Ježek (2007)

Czechoslovak Mathematical Journal

Slim groupoids are groupoids satisfying x ( y z ) x ̄ z . We find all simple slim groupoids and all minimal varieties of slim groupoids. Every slim groupoid can be embedded into a subdirectly irreducible slim groupoid. The variety of slim groupoids has the finite embeddability property, so that the word problem is solvable. We introduce the notion of a strongly nonfinitely based slim groupoid (such groupoids are inherently nonfinitely based) and find all strongly nonfinitely based slim groupoids with at most four...

Some decidable theories with finitely many covers which are decidable and algorithmically found

Cornelia Kalfa (1994)

Colloquium Mathematicae

In any recursive algebraic language, I find an interval of the lattice of equational theories, every element of which has finitely many covers. With every finite set of equations of this language, an equational theory of this interval is associated, which is decidable with decidable covers that can be algorithmically found. If the language is finite, both this theory and its covers are finitely based. Also, for every finite language and for every natural number n, I construct a finitely based decidable...

Some relations on the lattice of varieties of completely regular semigroups

Mario Petrich (2002)

Bollettino dell'Unione Matematica Italiana

On the lattice L ⁢ C ⁢ R of varieties of completely regular semigroups considered as algebras with the binary multiplication and unary inversion within maximal subgroups, we study the relations K l , K , K r , T l , T , T r , C and L . Here K is the kernel relation, T is the trace relation, T l and T r are the left and the right trace relations, respectively, K p = K ∩ T p for p ∈ l , r , C is the core relation and L is the local relation. We give an alternative definition for each of these relations P of the form U P V ⇔ U ∩ P ~ = V ∩ P ~ ( U , V ∈ L ( C R ) ) , for some subclasses P ~ of C ⁢ R ....

Special m-hyperidentities in biregular leftmost graph varieties of type (2,0)

Apinant Anantpinitwatna, Tiang Poomsa-ard (2009)

Discussiones Mathematicae - General Algebra and Applications

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies a term equation s ≈ t if the corresponding graph algebra A ( G ) ̲ satisfies s ≈ t. A class of graph algebras V is called a graph variety if V = M o d g Σ where Σ is a subset of T(X) × T(X). A graph variety V ' = M o d g Σ ' is called a biregular leftmost graph variety if Σ’ is a set of biregular leftmost term equations. A term equation s ≈ t is called an identity in a variety...

Subdirect products of certain varieties of unary algebras

Miroslav Ćirić, Tatjana Petković, Stojan Bogdanović (2007)

Czechoslovak Mathematical Journal

J. Płonka in [12] noted that one could expect that the regularization ℛ ( K ) of a variety K of unary algebras is a subdirect product of K and the variety D of all discrete algebras (unary semilattices), but is not the case. The purpose of this note is to show that his expectation is fulfilled for those and only those irregular varieties K which are contained in the generalized variety T D i r of the so-called trap-directable algebras.

The Galois correspondence between subvariety lattices and monoids of hpersubstitutions

Klaus Denecke, Jennifer Hyndman, Shelly L. Wismath (2000)

Discussiones Mathematicae - General Algebra and Applications

Denecke and Reichel have described a method of studying the lattice of all varieties of a given type by using monoids of hypersubstitutions. In this paper we develop a Galois correspondence between monoids of hypersubstitutions of a given type and lattices of subvarieties of a given variety of that type. We then apply the results obtained to the lattice of varieties of bands (idempotent semigroups), and study the complete sublattices of this lattice obtained through the Galois correspondence.

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