On linear algebraic semigroups III

Mohan S. Putcha

International Journal of Mathematics and Mathematical Sciences, 1981, vol. 4, 1-24

Abstract:

Using some results on linear algebraic groups, we show that every connected linear algebraic semigroup S contains a closed, connected diagonalizable subsemigroup T with zero such that E ( T ) intersects each regular J -class of S . It is also shown that the lattice ( E ( T ) , ≤ ) is isomorphic to the lattice of faces of a rational polytope in some ℝ n . Using these results, it is shown that if S is any connected semigroup with lattice of regular J -classes U ( S ) , then all maximal chains in U ( S ) have the same length.

Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:206137

DOI: 10.1155/S0161171281000513

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