Baer-Levi semigroups of partial transformations
21/10/2011 Sexta-feira, 21 de Outubro de 2011, 14 horas, Sala B2-01
Boorapa Singha (Department of Mathematics, Chiang Mai University, Thailand)
Instituto para a Investigação Interdisciplinar
Let $X$ be an infinite set, and let $q$ be a cardinal number with
$\aleph_0\leq q\leq |X|$. The Baer-Levi semigroup on $X$, noted
here $BL(q)$, is the set of all injective total transformation
$\alpha:X\rightarrow X$ such that $|X\setminus X\alpha| = q$. It
is known that $BL(q)$ is a right simple, right cancellative
semigroup without idempotents and it is a subsemigroup of the
partial Baer-Levi semigroup, denoted by $PS(q)$, consisting of all
injective partial transformations $\alpha$ of $X$ such that
$|X\setminus X\alpha| = q$. In this talk, we consider some
properties of $PS(q)$, concerned with its automorphisms and
maximal subsemigroups. We also study the natural partial order
defined by Mitsch on the symmetric inverse semigroup $I(X)$ and
$PS(q)$.
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