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On minimal ideals in semigroups with respect to their subsets. I.

Imrich Abrhan (1997)

Mathematica Bohemica

In the paper, the following concept are defined: (i) a minimal left (right, two-sided) ideal with respect to a subset B of a semigroup S , (ii) a kernel with respect to a subset B of a semigroup S , and their basic properties are investigated.

On modular elements of the lattice of semigroup varieties

Boris M. Vernikov (2007)

Commentationes Mathematicae Universitatis Carolinae

A semigroup variety is called modular if it is a modular element of the lattice of all semigroup varieties. We obtain a strong necessary condition for a semigroup variety to be modular. In particular, we prove that every modular nil-variety may be given by 0-reduced identities and substitutive identities only. (An identity u = v is called substitutive if the words u and v depend on the same letters and v may be obtained from u by renaming of letters.) We completely determine all commutative modular...

On Nilpotent Subsemigroups in some Matrix Semigroups

Ganyushkin, Olexandr, Mazorchuk, Volodymyr (2007)

Serdica Mathematical Journal

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.

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