Search results for "Identity component"
showing 4 items of 4 documents
Symmetric units and group identities
1998
In this paper we study rings R with an involution whose symmetric units satisfy a group identity. An important example is given by FG, the group algebra of a group G over a field F; in fact FG has a natural involution induced by setting g?g −1 for all group elements g∈G. In case of group algebras if F is infinite, charF≠ 2 and G is a torsion group we give a characterization by proving the following: the symmetric units satisfy a group identity if and only if either the group of units satisfies a group identity (and a characterization is known in this case) or char F=p >0 and 1) FG satisfies a polynomial identity, 2) the p-elements of G form a (normal) subgroup P of G and G/P is a Hamiltonia…
Shifting between cultural identities: The voice of preschool children
2018

 Aim. The purpose of this research is to capture the shift between two cultural identities, for a group of Romanian children enrolled in a German teaching preschool class, and to closely analyze the impact on cultural identity components.
 Methods. In this study 27 children, aged 3 to 6, were involved, together with their parents and two teachers. During one year of investigation, they were analyzed using participative observation, focus groups and in-depth interviews conducted in a public preschool.
 Results. The analysis reveals witch cultural identity components of this children undergo transformation, in what amount and with what impact considering the school environmen…
Group Identities on Units of Group Algebras
2000
Abstract 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 complete classification of such groups. For torsion groups this problem has already been settled in recent years.
Group algebras whose units satisfy a group identity
1997
Let F G FG be the group algebra of a torsion group over an infinite field F F . Let U U be the group of units of F G FG . We prove that if U U satisfies a group identity, then F G FG satisfies a polynomial identity. This confirms a conjecture of Brian Hartley.