# Commutative cancellative semigroups and rational vector spaces

Antonio M. Cegarra; Mario Petrich

Bollettino dell'Unione Matematica Italiana (2006)

- Volume: 9-B, Issue: 1, page 133-144
- ISSN: 0392-4041

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topCegarra, Antonio M., and Petrich, Mario. "Commutative cancellative semigroups and rational vector spaces." Bollettino dell'Unione Matematica Italiana 9-B.1 (2006): 133-144. <http://eudml.org/doc/289607>.

@article{Cegarra2006,

abstract = {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.},

author = {Cegarra, Antonio M., Petrich, Mario},

journal = {Bollettino dell'Unione Matematica Italiana},

language = {eng},

month = {2},

number = {1},

pages = {133-144},

publisher = {Unione Matematica Italiana},

title = {Commutative cancellative semigroups and rational vector spaces},

url = {http://eudml.org/doc/289607},

volume = {9-B},

year = {2006},

}

TY - JOUR

AU - Cegarra, Antonio M.

AU - Petrich, Mario

TI - Commutative cancellative semigroups and rational vector spaces

JO - Bollettino dell'Unione Matematica Italiana

DA - 2006/2//

PB - Unione Matematica Italiana

VL - 9-B

IS - 1

SP - 133

EP - 144

AB - 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.

LA - eng

UR - http://eudml.org/doc/289607

ER -

## References

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- GRILLET, P. A., Semigroups, An introduction to structure theory, Dekker, New York, 1995. MR1350793
- HAMILTON, H. B. - NORDAHL, T. E. - TAMURA, T., Commutative cancellative semigroups without idempotents, Pacific J. Math., 61 (1975), 441-456. Zbl0358.20073MR401954
- TAMURA, T., Basic study of $\U0001d511$-semigroups and their homomorphisms, Semigroup Forum, 8 (1974), 21-50. Zbl0275.20110MR374307DOI10.1007/BF02194744
- TAMURA, T., Commutative cancellative semigroups with nontrivial homomorphisms into nonnegative real numbers, J. Algebra, 76 (1982), 25-41. Zbl0486.20039MR659208DOI10.1016/0021-8693(82)90236-8

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