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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| Format: | Article |
| Language: | English |
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Wiley
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171281000513 |
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| _version_ | 1832553369727664128 |
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| author | Mohan S. Putcha |
| author_facet | Mohan S. Putcha |
| author_sort | Mohan S. Putcha |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f074c7b23e7d43daa8f63b37943ea08c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1981-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f074c7b23e7d43daa8f63b37943ea08c2025-02-03T05:54:13ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251981-01-014466769010.1155/S0161171281000513On linear algebraic semigroups IIIMohan S. Putcha0School of Physical and Mathematical Sciences, Department of Mathematlcs, North Carolina State University, Raleigh 27650, North Carolina, USAUsing 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.http://dx.doi.org/10.1155/S0161171281000513linear algebraic semigroupidempotentpolytope. |
| spellingShingle | Mohan S. Putcha On linear algebraic semigroups III International Journal of Mathematics and Mathematical Sciences linear algebraic semigroup idempotent polytope. |
| title | On linear algebraic semigroups III |
| title_full | On linear algebraic semigroups III |
| title_fullStr | On linear algebraic semigroups III |
| title_full_unstemmed | On linear algebraic semigroups III |
| title_short | On linear algebraic semigroups III |
| title_sort | on linear algebraic semigroups iii |
| topic | linear algebraic semigroup idempotent polytope. |
| url | http://dx.doi.org/10.1155/S0161171281000513 |
| work_keys_str_mv | AT mohansputcha onlinearalgebraicsemigroupsiii |