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Idempotents in Noetherian Group Rings

Published online by Cambridge University Press:  20 November 2018

Edward Formanek*
Affiliation:
Carleton University, Ottaway Ontario
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If G is a torsion–free group and F is a field, is the group ring F[G] a ring without zero divisors? This is true if G is an ordered group or various generalizations thereof - beyond this the question remains untouched. This paper proves a related result.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Atiyah, M. and Macdonald, I., Introduction to commutative algebra (Addison-Wesley, Reading, 1969).Google Scholar
2. Kaplansky, I., Fields and rings (Univ. of Chicago Press, Chicago, 1969).Google Scholar
3. Kaplansky, I., Commutative rings (Allyn and Bacon, Boston, 1970).Google Scholar
4. Kaplansky, I., Problems in the theory of rings revisited, Amer. Math. Monthly 77 (1970), 445454.Google Scholar
5. Montgomery, S., Left and right inverses in group algebras, Bull. Amer. Math. Soc. 75 (1969), 539540.Google Scholar
6. Passman, D. S., Idempotents in group rings, Proc. Amer. Math. Soc. 28 (1971), 371374.Google Scholar
7. Zalesskii, A. E., On a problem of Kaplansky, Dokl. Akad. Nauk SSSR 203 (1972), 749751 (Russian); Soviet Math. Dokl. 13 (1972), 449.Google Scholar