Abstract
We describe the local structure of an irreducible algebraic monoid M at an idempotent element e. When e is minimal, we show that M is an induced variety over the kernel MeM (a homogeneous space) with bre the two-sided stabilizer Me (a connected a ne monoid having a zero element and a dense unit group). This yields the irreducibility of stabilizers and centralizers of idempotents when M is normal, and criteria for normality and smoothness of an arbitrary monoid M . Also, we show that M is an induced variety over an abelian variety, with ber a connected a ne monoid having a dense unit group.
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