On classification of maximal nilpotent subsemigroups
نویسندگان
چکیده
We develop a general approach to the study of maximal nilpotent subsemigroups of finite semigroups. This approach can be used to recover many known classifications of maximal nilpotent subsemigroups, in particular, for the symmetric inverse semigroup, the symmetric semigroup, and the factor power of the symmetric group. We also apply this approach to obtain a classification of maximal nilpotent subsemigroups in the semigroup of binary relations and in certain 0-simple finite semigroups.
منابع مشابه
On nilpotent subsemigroups in some matrix semigroups
We describe maximal nilpotent subsemigroups of a given nilpotency class in the semigroup Ωn of all n × n real matrices with nonnegative coefficients and the semigroup Dn of all doubly stochastic real matrices.
متن کاملOn the semigroup of square matrices
We study the structure of nilpotent subsemigroups in the semigroup M(n,F) of all n × n matrices over a field, F, with respect to the operation of the usual matrix multiplication. We describe the maximal subsemigroups among the nilpotent subsemigroups of a fixed nilpotency degree and classify them up to isomorphism. We also describe isolated and completely isolated subsemigroups and conjugated e...
متن کاملOn the structure of two generalizations of the full inverse symmetric semigroup
We introduce two generalizations of the full inverse symmetric semigroup ISX — the inverse semigroups PIPX and P̃IPX . Both of these semigroups have the same set of elements and contain ISX . The binary operations on PIPX and P̃IPX are two natural generalizations of the multiplication of partial permutations and each of the considered operations coincides with this multiplication when restricted ...
متن کاملOn Kiselman’s semigroup
We study the algebraic properties of the series Kn of semigroups, which is inspired by [Ki] and has origins in convexity theory. In particular, we describe Green’s relations on Kn, prove that there exists a faithful representation of Kn by n × n matrices with non-negative integer coefficients (and even explicitly construct such a representation), and prove that Kn does not admit a faithful repr...
متن کاملCombinatorics of Words and Semigroup Algebras Which Are Sums of Locally Nilpotent Subalgebras
We construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. As all previously known examples, our examples are contracted semigroup algebras and the underlying semigroups are unions of locally nilpotent subsemigroups. In our constructions we make more transparent than in the past the close relationship between the cons...
متن کامل