Maximal subsemigroups and finiteness conditions on transformation semigroups with fixed sets | Zendy

Yanisa Chaiya | Zendy; Preeyanuch Honyam | Zendy; Jintana Sanwong | Zendy

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Maximal subsemigroups and finiteness conditions on transformation semigroups with fixed sets

Author(s) -

Yanisa Chaiya,

Preeyanuch Honyam,

Jintana Sanwong

Publication year - 2017

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1507-7

Subject(s) - mathematics , combinatorics , set (abstract data type) , semigroup , transformation (genetics) , monoid , unit (ring theory) , discrete mathematics , pure mathematics , biochemistry , chemistry , gene , mathematics education , computer science , programming language

Let Y be a fixed subset of a nonempty set X and let Fix(X,Y ) be the set of all self maps on X which fix all elements in Y . Then under the composition of maps, Fix(X,Y ) is a regular monoid. In this paper, we prove that there are only three types of maximal subsemigroups of Fix (X,Y ) and these maximal subsemigroups coincide with the maximal regular subsemigroups when X \ Y is a finite set with |X \ Y | ≥ 2. We also give necessary and sufficient conditions for Fix(X,Y ) to be factorizable, unit-regular, and directly finite.

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