文章基本信息

标题：On linear algebraic semigroups III
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作者：Mohan S. Putcha
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1981
卷号：4
DOI：10.1155/S0161171281000513
出版社：Hindawi Publishing Corporation
摘要：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.