On linear algebraic semigroups III

[摘要] Using some results on linear algebraic groups, we show that every connectedlinear algebraic semigroupScontains a closed, connected diagonalizable subsemigroupTwith zero such thatE(T)intersects each regularJ-class ofS. It is also shown that the lattice(E(T),≤)is isomorphic to the lattice of faces of a rational polytope in someℝn. Using these results, it is shown that ifSis any connected semigroup with lattice of regularJ-classesU(S), then all maximal chains inU(S)have the same length.

[学科分类] 数学（综合）