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Septembro, 10 - Bob Sullivan

A major result in semigroup theory says that certain algebraic semigroups are isomorphic to semigroups of rectangular matrices, provided the matrices are multiplied using a fixed 'sandwich matrix' $ P$: that is, $ A*B = APB$, for all matrices $ A$ and $ B$ in the semigroup.

In 1967, Magill defined a semigroup of transformations in a similar way: namely, suppose $ X$ and $ Y$ are sets, let $ T(X,Y)$ be the set of all mappings from $ X$ into $ Y$, fix some $ p$ in $ T(Y,X)$, and define $ *$ on $ T(X,Y)$ by: $ f*g=fpg$. This produces a semigroup, and Magill determined when it is regular. Since then, some Thai mathematicians and I have extended this idea to partial transformations of arbitrary sets and vector spaces, and determined when such semigroups satisfy other algebraic properties. I will discuss some of that work in this talk.

 
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