On linear algebraic semigroups III
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 o...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171281000513 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |