On linear algebraic semigroups. III.
In the paper, the following concept are defined: (i) a minimal left (right, two-sided) ideal with respect to a subset of a semigroup , (ii) a kernel with respect to a subset of a semigroup , and their basic properties are investigated.
2000 Mathematics Subject Classification: 20M20, 20M10.We describe maximal nilpotent subsemigroups of a given nilpotency class in the semigroup Ωn of all n × n real matrices with non-negative coefficients and the semigroup Dn of all doubly stochastic real matrices.