Epimorphisms, dominions and varieties of semigroups.
Epimorphisms in some groupoid varieties
Epimorphisms of inverse semigroups of homeomorphisms between closed subsets.
Epimorphisms, permutation identities and finite semigroups.
Epis are onto for generalized inverse semigroups.
Epis from locally inverse semigroups are onto.
Equalizers and coactions of groups
If f:G → H is a group homomorphism and p,q are the projections from the free product G*H onto its factors G and H respectively, let the group be the equalizer of fp and q:G*H → H. Then p restricts to an epimorphism . A right inverse (section) of is called a coaction on G. In this paper we study and the sections of . We consider the following topics: the structure of as a free product, the restrictions on G resulting from the existence of a coaction, maps of coactions and the resulting...
Equational description of pseudovarieties of homomorphisms
The notion of pseudovarieties of homomorphisms onto finite monoids was recently introduced by Straubing as an algebraic characterization for certain classes of regular languages. In this paper we provide a mechanism of equational description of these pseudovarieties based on an appropriate generalization of the notion of implicit operations. We show that the resulting metric monoids of implicit operations coincide with the standard ones, the only difference being the actual interpretation of pseudoidentities....
Equational description of pseudovarieties of homomorphisms
The notion of pseudovarieties of homomorphisms onto finite monoids was recently introduced by Straubing as an algebraic characterization for certain classes of regular languages. In this paper we provide a mechanism of equational description of these pseudovarieties based on an appropriate generalization of the notion of implicit operations. We show that the resulting metric monoids of implicit operations coincide with the standard ones, the only difference being the actual interpretation of pseudoidentities. As...
Equational theories of some almost unary groupoids
Equations and dot-depth one.
Équations dans les monoïdes libres
Après une introduction de caractère historique, l'auteur expose succinctement les principaux résultats qu'il a obtenus (thèse, Paris 1969) dans le domaine jusqu'alors pratiquement inexploré des équations dans les monoïdes libres.
Equations defining Schubert varieties and Frobenius splittings of diagonals
Equations fonctionnelles et recherche de sous-groupes.
Equations in groups, with special emphasis on localization and torsion - II
Equations in simple matrix groups: algebra, geometry, arithmetic, dynamics
We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods: group-theoretic and coming from algebraic and arithmetic geometry, number theory, dynamical systems and computer algebra. Our focus is on interrelations of these machineries which led to numerous spectacular achievements, including solutions of several long-standing problems.
Equations of some wonderful compactifications
De Concini and Procesi have defined the wonderful compactification of a symmetric space where is a complex semisimple adjoint group and the subgroup of fixed points of by an involution . It is a closed subvariety of a Grassmannian of the Lie algebra of . In this paper we prove that, when the rank of is equal to the rank of , the variety is defined by linear equations. The set of equations expresses the fact that the invariant alternate trilinear form on vanishes on the -eigenspace...
Equations on the semidirect product of a finite semilattice by a finite commutative monoid.
Equiangular Lines, the Graph Extension Theorem, and Transfer in Triply Transitive Groups.
Equidecomposability of Polyhedra with Reference to Crystallographic Groups.