Matematičeskie zametki, Tome 3 (1968) no. 6, pp. 657-662
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E. S. Lyapin. Defining relations of semigroups of all directed transformations of an ordered finite set. Matematičeskie zametki, Tome 3 (1968) no. 6, pp. 657-662. http://geodesic.mathdoc.fr/item/MZM_1968_3_6_a4/
@article{MZM_1968_3_6_a4,
author = {E. S. Lyapin},
title = {Defining relations of semigroups of all directed transformations of an~ordered finite set},
journal = {Matemati\v{c}eskie zametki},
pages = {657--662},
year = {1968},
volume = {3},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_6_a4/}
}
TY - JOUR
AU - E. S. Lyapin
TI - Defining relations of semigroups of all directed transformations of an ordered finite set
JO - Matematičeskie zametki
PY - 1968
SP - 657
EP - 662
VL - 3
IS - 6
UR - http://geodesic.mathdoc.fr/item/MZM_1968_3_6_a4/
LA - ru
ID - MZM_1968_3_6_a4
ER -
%0 Journal Article
%A E. S. Lyapin
%T Defining relations of semigroups of all directed transformations of an ordered finite set
%J Matematičeskie zametki
%D 1968
%P 657-662
%V 3
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1968_3_6_a4/
%G ru
%F MZM_1968_3_6_a4
The semigroup $\mathfrak A$ of all transformations $X$ of a finite (partially) ordered set $\Omega$, such that $\alpha\le X\alpha$ for all $\alpha\in\Omega$, is considered. All possible generating sets of a $\Omega$ are elucidated. Only one of those sets is irreducible. A system of defining relations is found for that generating set.
