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: 0392-4033

Abstract

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Representing a commutative cancellative subarchimedean semigroup S as i ( G , I ) , we consider Hom ( S , ) and Hom  ( G , ) , 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.

How to cite

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Cegarra, 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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  1. CEGARRA, A. M. - PETRICH, M., Categories of representations of a class of commutative cancellative semigroups, Algebra Colloq., 8 (2001), 361-380. Zbl1001.20052MR1865117
  2. CEGARRA, A. M. - PETRICH, M., The rank of a commutative cancellative semigroup, Acta Math. Hung., 107 (1-2) (2005), 71-75. Zbl1076.20049MR2148936DOI10.1007/s10474-005-0179-x
  3. FUCHS, L., Infinite abelian groups I, Academic Press, New York, San Francisco, London, 1974. Zbl0338.20063MR348006
  4. GRILLET, P. A., Semigroups, An introduction to structure theory, Dekker, New York, 1995. MR1350793
  5. HAMILTON, H. B. - NORDAHL, T. E. - TAMURA, T., Commutative cancellative semigroups without idempotents, Pacific J. Math., 61 (1975), 441-456. Zbl0358.20073MR401954
  6. TAMURA, T., Basic study of 𝔑 -semigroups and their homomorphisms, Semigroup Forum, 8 (1974), 21-50. Zbl0275.20110MR374307DOI10.1007/BF02194744
  7. 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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