Group algebras with symmetric units satisfying a group identity
β Scribed by S.K. Sehgal; A. Valenti
- Publisher
- Springer
- Year
- 2005
- Tongue
- English
- Weight
- 167 KB
- Volume
- 119
- Category
- Article
- ISSN
- 0025-2611
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π SIMILAR VOLUMES
Let R = denote the group of units of an associative algebra R over an infinite field F. We prove that if R is unitarily generated by its nilpotent elements, then R = satisfies a group identity precisely when R satisfies a nonmatrix polynomial identity. As an application, we examine the group algebra
Let U be the group of units of the group algebra FG of a group G over a field F. Suppose that either F is infinite or G has an element of infinite order. We characterize groups G so that U satisfies a group identity. Under the assumption that G modulo the torsion elements is nilpotent this gives a c