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- Title
On algebraic semigroups and monoids, II.
- Authors
Brion, Michel
- Abstract
Consider an algebraic semigroup S and its closed subscheme of idempotents, E( S). When S is commutative, we show that E( S) is finite and reduced; if in addition S is irreducible, then E( S) is contained in a smallest closed irreducible subsemigroup of S, and this subsemigroup is an affine toric variety. It follows that E( S) (viewed as a partially ordered set) is the set of faces of a rational polyhedral convex cone. On the other hand, when S is an irreducible algebraic monoid, we show that E( S) is smooth, and its connected components are conjugacy classes of the unit group.
- Subjects
SEMIGROUPS (Algebra); MONOIDS; IDEMPOTENTS; COMMUTATIVE algebra; POLYHEDRAL functions; CONJUGACY classes
- Publication
Semigroup Forum, 2014, Vol 88, Issue 1, p250
- ISSN
0037-1912
- Publication type
Article
- DOI
10.1007/s00233-013-9528-1