We investigate partial monoid actions, in the sense of Megrelishvili and Schroder [12]. These are equivalent to a class of premorphisms, which we call strong premorphisms. We describe two distinct… Expand

Left restriction semigroups are a class of semigroups which generalise inverse semigroups and which emerge very naturally from the study of partial transformations of a set. Consequently, they have… Expand

The Ehresmann–Schein–Nambooripad (ESN) Theorem, stating that the category of inverse semigroups and morphisms is isomorphic to the category of inductive groupoids and inductive functors, is a… Expand

Abstract We introduce partial actions of weakly left E-ample semigroups, thus extending both the notion of partial actions of inverse semigroups and that of partial actions of monoids. Weakly left… Expand

This work gives a complete description of Green's D relation for the multiplicative semigroup of all n × n tropical matrices and shows that the matrix duality map induces an isometry (with respect to the Hilbert projective metric) between the projective row space and projective column space of any tropical matrix.Expand

The education of Ada, Countess of Lovelace before 1840 is looked at, which encompassed older traditions of practical geometry; newer textbooks influenced by continental approaches; wide reading; and a fascination with machinery.Expand

The Ehremann--Schein--Nambooripad Theorem expresses the fundamental connection between the notions of inverse semigroups and inductive groupoids, which exists because these concepts provide two… Expand

In the history of mathematics, the algebraic theory of semigroups is a relative new-comer, with the theory proper developing only in the second half of the twentieth century. Before this, however,… Expand