Geodesic
A characterization of subdirectly irreducible acts
Prikladnaâ diskretnaâ matematika, no. 1 (2015), pp. 5-16

Voir la notice de l'article provenant de la source Math-Net.Ru

The subdirectly irreducible acts (automata) over semigroups are investigated. In 1974, E. N. Roiz proved that such acts have at most two zeros. Here, we characterize subdirectly irreducible acts with two zeros and reduce the characterization of an act with one zero or without zeros to the structure of its least non-trivial subact. We fully characterize the subdirectly irreducible acts over rectangular bands. As the corollaries we have a characterization of subdirectly irreducible acts over right zero semigroups and the Moghaddassi's result about acts over left zero semigroups.
Keywords: act over semigroup, subdirectly irreducible act, rectangular band. 
@article{PDM_2015_1_a0,
     author = {I. B. Kozhukhov and A. R. Haliullina},
     title = {A characterization of subdirectly irreducible acts},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {5--16},
     publisher = {mathdoc},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2015_1_a0/}
}
TY  - JOUR
AU  - I. B. Kozhukhov
AU  - A. R. Haliullina
TI  - A characterization of subdirectly irreducible acts
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2015
SP  - 5
EP  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2015_1_a0/
LA  - ru
ID  - PDM_2015_1_a0
ER  - 
%0 Journal Article
%A I. B. Kozhukhov
%A A. R. Haliullina
%T A characterization of subdirectly irreducible acts
%J Prikladnaâ diskretnaâ matematika
%D 2015
%P 5-16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2015_1_a0/
%G ru
%F PDM_2015_1_a0
I. B. Kozhukhov; A. R. Haliullina. A characterization of subdirectly irreducible acts. Prikladnaâ diskretnaâ matematika, no. 1 (2015), pp. 5-16. http://geodesic.mathdoc.fr/item/PDM_2015_1_a0/