International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 4, Pages 667-690
doi:10.1155/S0161171281000513
On linear algebraic semigroups III
School of Physical and Mathematical Sciences, Department of Mathematlcs, North Carolina State University, Raleigh 27650, North Carolina, USA
Received 18 July 1980
Copyright © 1981 Mohan S. Putcha. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 ℝn. 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.