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Polynomial Ideals in Group Rings

Published online by Cambridge University Press:  20 November 2018

M. M. Parmenter ,
I. B. S. Passi  and
S. K. Sehgal
M. M. Parmenter
Affiliation:
University of Alberta, Edmonton, Alberta
I. B. S. Passi
Affiliation:
University of Alberta, Edmonton, Alberta
S. K. Sehgal
Affiliation:
University of Kurukshetra, Kurukshetra, India
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Letf(x1, x2, … , xn) be a polynomial in n non-commuting variables x1, x2, … , xn and their inverses with coefficients in the ring Z of integers, i.e. an element of the integral group ring of the free group on X1, x2, … , xn. Let R be a commutative ring with unity, G a multiplicative group and R(G) the group ring of G with coefficients in R.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 6 , December 1973 , pp. 1174 - 1182
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Connell, I. G., On the group ring, Can. J. Math. 15 (1963), 650–685.Google Scholar
2. Hartley, B., The residual nilpotence of wreath products, Proc. London Math. Soc. 20 (1970), 365–392.Google Scholar
3. Losey, G., On group algebras of p-groups, Michigan Math. J. 7 (1960), 237–240.Google Scholar
4. Mital, J. N., On residual nilpotence, J. London Math. Soc. 2 (1970), 337–345.Google Scholar
5. Parmenter, M. M., On a theorem of Bovdi, Can. J. Math. 23 (1971), 929–932.Google Scholar
6. Passi, I. B. S., Polynomial maps on groups, J. Algebra 9 (1968), 121–151.Google Scholar
7. Sandling, R., The modular group rings of p-groups, Ph.D. Thesis, University of Chicago, 1969.Google Scholar
8. Sehgal, S. K., Lie properties in group algebras, Proceedings of the conference on “Orders, Group Rings and Related Topics”, Ohio State University, 1972, Springer-Verlag (to appear).Google Scholar