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International Journal of Mathematics and Mathematical Sciences - Volume 4 1981, Issue 4, Pages 667-690

School of Physical and Mathematical Sciences, Department of Mathematlcs, North Carolina State University, Raleigh 27650, North Carolina, USA

Received 18 July 1980

Copyright © 1981 Hindawi Publishing Corporation. 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 connectedlinear algebraic semigroup S contains a closed, connected diagonalizable subsemigroup T with zero such that ET intersects each regular J-class of S. It is also shown that the lattice ET,≤ 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 US, then all maximal chains in US have the same length.





Author: Mohan S. Putcha

Source: https://www.hindawi.com/



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