Open AccessEmbedding theorems and maximal subsemigroups of some linear transformation semigroups with restricted range
Author(s) -
Worachead Sommanee
Publication year - 2021
Publication title -
ukrains’kyi matematychnyi zhurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v73i12.1289
Subject(s) - mathematics , semigroup , embedding , vector space , subspace topology , linear map , linear subspace , pure mathematics , discrete mathematics , transformation (genetics) , field (mathematics) , range (aeronautics) , mathematical analysis , computer science , gene , materials science , biochemistry , artificial intelligence , composite material , chemistry
UDC 512.64Let be a vector space and let denote the semigroup (under composition) of all linear transformations from into . For a fixed subspace of , let be the semigroup consisting of all linear transformations from into . It is known that is the largest regular subsemigroup of . In this paper, we prove that any regular semigroup can be embedded in with and , and determine all the maximal subsemigroups of when is a finite dimensional subspace of over a finite field.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom