Open AccessAbundance of $E$-order-preserving transformation semigroups
Author(s) -
Lei Sun,
Xuefeng Han
Publication year - 2015
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-1412-37
Subject(s) - mathematics , transformation (genetics) , order (exchange) , abundance (ecology) , pure mathematics , ecology , chemistry , business , biology , biochemistry , finance , gene
Let T X be the full transformation semigroup on anite totally ordered set X = f 1 < 2 < ::: < ng ( n 3) and E be a nontrivial equivalence relation on X. In this paper, we consider a subsemigroup of T X dened by EOPX = f f 2 T X : 8 x;y 2 X; ( x;y) 2 E;xy ) ( f ( x) ;f ( y)) 2 E;f ( x) f ( y) g and present a necessary and sufficient condition under which the semigroup EOPX is abundant.
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