The Algebraic Theory of Semigroups, Vol. I. By A. H. Clifford and G. B. Preston. Pp. xv + 224. $10.60. 1961. (American Mathematical Society, Providence.)

Introduction to semigroup theory

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Classical finite transformation semigroups

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Introduction to Boolean algebras

Pseudogroups and their étale groupoids

We obtain presentations for the Brauer monoid, the partial analogue of the Brauer monoid, and for the greatest factorizable inverse submonoid of the dual symmetric inverse monoid. In all three cases we apply the same approach, based on the realization of all these monoids as Brauer-type monoids.

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On presentations of Brauer-type monoids

We give, in terms of (generalized) cyclic types, a criterion for two elements of T-n, T-n, IS(N), B-n, PBn, and C-n to be conjugate with respect to the conjugation defined as the transitive closure of the xy similar to yx relation.

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On conjugation in some transformation and Brauer-type semigroups

We compare three approaches to the notion of conjugacy for semigroups, the first one via the transitive closure of the uv∼vu relation, the second one via an action of inverse semigroups on themselves by partial transformations, and the third one via characters of finite-dimensional representations.

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On three approaches to conjugacy in semigroups

We establish two theorems that refine the classical Stone duality between generalized Boolean algebras and locally compact Boolean spaces. In the first theorem, we prove that the category of left-handed skew Boolean algebras whose morphisms are proper skew Boolean algebra homomorphisms is equivalent to the category of etale spaces over locally compact Boolean spaces whose morphisms are etale space cohomomorphisms over continuous proper maps. In the second theorem, we prove that the category of left-handed skew Boolean ${\bigcap}$-algebras whose morphisms are proper skew Boolean ${\bigcap}$-algebra homomorphisms is equivalent to the category of etale spaces with compact clopen equalizers over locally compact Boolean spaces whose morphisms are injective etale space cohomomorphisms over continuous proper maps.

A refinement of Stone duality to skew Boolean algebras

We compare three approaches to the notion of conjugacy for semigroups, the first one via the transitive closure of the $uv\sim vu$ relation, the second one via an action of inverse semigroups on themselves by partial transformations, and the third one via characters of finite-dimensional representations.

Ganna Kudryavtseva

Papers

On presentations of Brauer-type monoids

On conjugation in some transformation and Brauer-type semigroups

On three approaches to conjugacy in semigroups

A refinement of Stone duality to skew Boolean algebras

On three approaches to conjugacy in semigroups