Green's-like relations on algebras and varieties.
Group conjugation has non-trivial LD-identities
We show that group conjugation generates a proper subvariety of left distributive idempotent groupoids. This subvariety coincides with the variety generated by all cancellative left distributive groupoids.
Gruppi con identità semigruppali: su una congettura di M. V. Sapir
M. V. Sapir ha formulato la seguente congettura: non esiste un semigruppo infinito, finitamente generabile, soddisfacente l'identità e immagine omomorfa di un sottosemigruppo di un gruppo nilpotente. Se ciò vale, ogni gruppo risolubile con una base finita per le sue identità semigruppali è abeliano o di esponente finito. In questo lavoro si prova la congettura di Sapir quando l'interderivato è periodico o se è -generato e è periodico.
HNN extensions of semigroups.
How much semigroup structure is needed to encode graphs ?
Hyperassociative varieties of semigroups.
Identities valid globally in semigroups.
Injectives in varieties of completely simple semigroups.
Inverse semigroup varieties generated by E-unitary semigroups.
Inverse semigroup varieties with the amalgamation property.
Irreducible Belousov equations on quasigroups
Krohn-Rhodes complexity pseudovarieties are not finitely based
We prove that the pseudovariety of monoids of Krohn-Rhodes complexity at most is not finitely based for all . More specifically, for each pair of positive integers , we construct a monoid of complexity , all of whose -generated submonoids have complexity at most .
Krohn-Rhodes complexity pseudovarieties are not finitely based
We prove that the pseudovariety of monoids of Krohn-Rhodes complexity at most n is not finitely based for all n>0. More specifically, for each pair of positive integers n,k, we construct a monoid of complexity n+1, all of whose k-generated submonoids have complexity at most n.
Lattice-theoretically characterized classes of finite bands
There are investigated classes of finite bands such that their subsemigroup lattices satisfy certain lattice-theoretical properties which are related with the cardinalities of the Green’s classes of the considered bands, too. Mainly, there are given disjunctions of equations which define the classes of finite bands.
Locally finite M-solid varieties of semigroups
An algebra of type τ is said to be locally finite if all its finitely generated subalgebras are finite. A class K of algebras of type τ is called locally finite if all its elements are locally finite. It is well-known (see [2]) that a variety of algebras of the same type τ is locally finite iff all its finitely generated free algebras are finite. A variety V is finitely based if it admits a finite basis of identities, i.e. if there is a finite set σ of identities such that V = ModΣ, the class of...
Matrix identities involving multiplication and transposition
We study matrix identities involving multiplication and unary operations such as transposition or Moore–Penrose inversion. We prove that in many cases such identities admit no finite basis.
Maximal submonoids of monoids of hypersubstitutions
For a monoid M of hypersubstitutions, the collection of all M-solid varieties forms a complete sublattice of the lattice L(τ) of all varieties of a given type τ. Therefore, by the study of monoids of hypersubstitutions one can get more insight into the structure of the lattice L(τ). In particular, monoids of hypersubstitutions were studied in [9] as well as in [5]. We will give a complete characterization of all maximal submonoids of the monoid Reg(n) of all regular hypersubstitutions of type τ...
Minimal non-finitely based monoids [Book]
Monoid varieties defined by xn+1 = ... are local.
Monoides de comptage et langages rationnels.