Commutative cancellative semigroups and rational vector spaces

Cegarra, Antonio M.; Petrich, Mario

Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006), p. 133-144 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

Representing a commutative cancellative subarchimedean semigroup $S$ as $\mathbb{N}_{i}(G,I)$ , we consider $\text{Hom}(S,\mathbb{Q})$ and $\text{Hom }(G,\mathbb{Q})$ , where Q is the additive group of rational numbers. These sets can be given the structure of rational vector spaces. Suitable isomorphic copies of these vector spaces are found by means of certain functions related to some mappings introduced by T. Tamura.

Rappresentando un semigruppo commutativo cancellativo subarchimedeo $S$ e come $\mathbb{N}_{i}(G,I)$ , consideriamo $\text{Hom}(S,\mathbb{Q})$ e $\text{Hom }(G,\mathbb{Q})$ , dove $\mathbb{Q}$ è il gruppo additivo dei numeri razionali. Questi insiemi possono essere muniti di una struttura di spazio vettoriale razionale. Si trovano convenienti copie isomorfe di questi spazi vettoriali con uso di funzioni in relazione a certe applicazioni introdotte da T. Tamura.

Publié le : 2006-02-01

MR 2204904 | Zbl 1147.20317

@article{BUMI_2006_8_9B_1_133_0,
     author = {Antonio M. Cegarra and Mario Petrich},
     title = {Commutative cancellative semigroups and rational vector spaces},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {9-A},
     year = {2006},
     pages = {133-144},
     zbl = {1147.20317},
     mrnumber = {2204904},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2006_8_9B_1_133_0}
}

Cegarra, Antonio M.; Petrich, Mario. Commutative cancellative semigroups and rational vector spaces. Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006) pp. 133-144. http://gdmltest.u-ga.fr/item/BUMI_2006_8_9B_1_133_0/

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