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Details van artikel 9 van 27 gevonden artikelen
| Titel: |
Formal power series representations of free exponential groups |
| Auteur: |
Gaglione, A. M. Myasnikov, A. G. Remeslennikov, V. N. Spellman, D. |
| Verschenen in: |
Communications in algebra |
| Paginering: | Jaargang 25 (1997) nr. 2 pagina's 631-648 |
| Jaar: |
1997 |
| Inhoud: |
A classical result of Magnus asserts that a free group F has a faithful representation in the group of units of a ring of non-commuting formal power series with integral coefficients. We generalize this result to the category of A-groups, where A is an associative ring or an Abelian group. We say that a free A-group FA has a faithful Magnus representation if there is a ring B containing A as an additive subgroup (or a subring) such that FA is faithfully represented (exactly as in Magnus' classical result in the case A = Z)in the group of units of the ring of formal power series in non-communting indeterminater over B.The three principal results are: (I) If A is a torsion free Abelian group and FA is a free A-groupp of Lyndon' type, then FA has a faithful Magnus representation; (II) If A is an ω-residually Z ring, then FA has a faithful Magnus representation;(III) for every nontrivial torsion-free Abelian group A, FA has a faithful Magnus representation in B[[Y]] for a suitable ring B in and only if FQ has a faithful Magnus representation in Q[[Y]]. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 9 van 27 gevonden artikelen
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