Geodesic
Properties of Integers and Finiteness Conditions for Semigroups
Séminaire lotharingien de combinatoire, Tome 26 (1991)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

Let h and k be integers greater than 1; we prove that the following statements are equivalent: 1) the direct product of h copies of the additive semigroup of non-negative integers is not k-repetitive; 2) if the direct product of h finitely generated semigroups is k-repetitive, then one of them is finite. Using this and some results of Dekking and Pleasants on infinite words, we prove that certain repetitivity properties are finiteness conditions for finitely generated semigroups. 

@article{SLC_1991_26_a10,
     author = {Giuseppe Pirillo},
     title = {Properties of {Integers} and {Finiteness} {Conditions} for {Semigroups}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {26},
     year = {1991},
     url = {http://geodesic.mathdoc.fr/item/SLC_1991_26_a10/}
}
TY  - JOUR
AU  - Giuseppe Pirillo
TI  - Properties of Integers and Finiteness Conditions for Semigroups
JO  - Séminaire lotharingien de combinatoire
PY  - 1991
VL  - 26
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_1991_26_a10/
ID  - SLC_1991_26_a10
ER  - 
%0 Journal Article
%A Giuseppe Pirillo
%T Properties of Integers and Finiteness Conditions for Semigroups
%J Séminaire lotharingien de combinatoire
%D 1991
%V 26
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_1991_26_a10/
%F SLC_1991_26_a10
Giuseppe Pirillo. Properties of Integers and Finiteness Conditions for Semigroups. Séminaire lotharingien de combinatoire, Tome 26 (1991). http://geodesic.mathdoc.fr/item/SLC_1991_26_a10/