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Torsion-free Abelian Groups, Valuations and Twisted Group Rings

Published online by Cambridge University Press:  20 November 2018

Gervasio G. Bastos  and
T. M. Viswanathan
Gervasio G. Bastos
Affiliation:
Departamento de Matemática Universidade Federal do Ceará 60.000 Fortaleza, Brasíl University of North Carolina at Charlotte, CharlotteNC 28223
T. M. Viswanathan
Affiliation:
Imecc, Departamento de Matemática, Universidade Estadual de Campinas13.081 Campinas, S. P., Brasíl University of North Carolina at Charlotte, CharlotteNC 28223
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Abstract

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Anderson and Ohm have introduced valuations of monoid rings k[Γ] where k is a field and Γ a cancellative torsion-free commutative monoid. We study the residue class fields in question and solve a problem concerning the pure transcendence of the residue fields.

Keywords

13A1820K2013G05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 2 , 01 June 1988 , pp. 139 - 146
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Anderson, D. F. and Ohm, J., Valuations and semi-valuations of graded domains, Math. Ann. 256 (1981), pp. 145–156.Google Scholar
2. Bourbaki, N., Elements de Mathématique, Livre II, Algèbre. Chap. 5 Corps Commutatifs, 2nd ed., Herman, Paris, 1959.Google Scholar
3. Fuchs, L., Infinite Abelian Groups, vol. 1, Academic Press, New York and London, 1970.Google Scholar
4. Gilmer, R., Commutative Semigroup Rings, The University of Chicago Press, Chicago and London, 1984.Google Scholar
5. Gilmer, R. and Parker, T., Divisibility properties in semigroup rings, Mich. Math. J. 21 (1974), pp. 65–86.Google Scholar
6. Karpilovsky, G., Commutative Group Algebras, Dekker, New York, 1983.Google Scholar
7. Močkoř, J., Groups of Divisibility, D. Reidel Publishing Company, Boston, 1983.Google Scholar