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
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- 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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