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September, 15 - Suzana Mendes-Gonçalves (CMAT-UM)

Given an infinite-dimensional vector space $ V$, we consider the semigroup $ GS(m,n)$ consisting of all injective linear $ \alpha:V\to V$ for which $ codim\, ran\, \alpha=n$ where $ \dim V=m\geq n\geq\aleph_0$. This is a linear version of the well-known Baer-Levi semigroup $ BL(p,q)$ defined on an infinite set $ X$ where $ \vert
X\vert=p\geq q\geq\aleph_0$. Recently, Prof R P Sullivan and I showed that, although the basic properties of $ GS(m,n)$ are the same as those of $ BL(p,q)$, the two semigroups are never isomorphic. We also determined all left ideals of $ GS(m,n)$ and some of its maximal subsemigroups: in this, we followed previous work on $ BL(p,q)$ by Sutov (1966) and Sullivan (1978) as well as Levi and Wood (1984). I will discuss some of that work in this talk.
 
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