Prime rings whose units satisfy a group identity

Mauceri, S.; Misso, P.

doi:10.1080/00927870008827161

Cited by 5 publications

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“…Hence A is a subdirect product of domains. This result generalizes recent results obtained in [11,16] and as an application we also obtain an easier proof of a result obtained in [8] on GI-group algebras of arbitrary groups over an infinite field. The result on reduced rings is an important tool in proving the main result of this article: a characterization of GI-semigroup algebras k[S] over infinite fields k and semigroups S generated by periodic elements.…”

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confidence: 89%

“…Hence, as an immediate application of Theorem 1.3, we obtain the first part of the following corollary, which generalizes some recent results. Corollary 1.4 [11,14,16,17]. Let D be an infinite commutative domain and A a D-algebra so that U(A) satisfies a group identity.…”

Section: Preliminariesmentioning

confidence: 99%

“…A natural generalization of Hartley's conjecture was then also proved for other algebras, such as twisted group algebras [13], locally finite algebras [16] and group algebras of arbitrary groups [7,8]. Also a classification of certain other GI-rings has been obtained [3,7,8,15,20].…”

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confidence: 98%

“…In recent papers [2,3,14,16,17] one then studied the algebraic structure of GI-rings. In [3] it was proved that the indices of nilpotent elements of a semiprime GI-ring R are bounded by a constant depending on the group identity.…”

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confidence: 99%

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On group identities for the unit group of algebras and semigroup algebras over an infinite field

Dooms¹,

Jespers²,

Juriaans³

2005

Journal of Algebra

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Let k be an infinite field. We fully describe when the unit group of a semigroup algebra k[S] of a semigroup S generated by finitely many periodic elements satisfies a group identity. This and some other recent results are proved by first showing that semiprime k-algebras generated by units are necessarily reduced whenever their unit group satisfies a group identity.  2004 Elsevier Inc. All rights reserved.The unit group U(R) of a ring R with unity 1 is said to satisfy a group identity (we call R a GI-ring for short) if there exists a non-trivial word w(x 1 , . . . , x n ) in the free group generated by x 1 , . . . , x n such that w(u 1 , . . . , u n ) = 1 for all u 1 , . . . , u n ∈ U(R).We start with a brief overview of some recent results on this topic. As a consequence of a more general result, Valitskas in [23] proved that if A is an algebra over an infinite field ✩ Research partially supported by the Onderzoeksraad of Vrije Universiteit Brussel and Fonds voor Wetenschappelijk Onderzoek (Vlaanderen), Flemish-Polish bilateral agreement BIL 01/31, FAPESP-Brazil and CNPq-Brazil (Proc. 300652/95-0).

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confidence: 89%