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Group Identities on Units and Symmetric Units of Group Rings
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Catalogue Information
Field name
Details
Dewey Class
512.46
Title
Group Identities on Units and Symmetric Units of Group Rings ([Ebook]) / by Gregory T. Lee.
Author
Lee, Gregory T.
Other name(s)
SpringerLink (Online service)
Publication
London : Springer London , 2010.
Physical Details
XII, 196 pages : online resource.
Series
Algebra and Applications
; 12
ISBN
9781849965040
Summary Note
Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid 1990s, a conjecture of Hartley was verified, namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed. Since the late 1990s, many papers have been devoted to the study of the symmetric units; that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which these symmetric units satisfy a group identity have now been determined. This book presents these results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies several particular group identities of interest.:
Contents note
Group Identities on Units of Group Rings -- Group Identities on Symmetric Units -- Lie Identities on Symmetric Elements -- Nilpotence of U(FG) and U+(FG) -- The Bounded Engel Property -- Solvability of U(FG) and U+(FG) -- Further Reading -- Some Results on Prime and Semiprime Rings.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site
http://dx.doi.org/10.1007/978-1-84996-504-0
Links to Related Works
Subject References:
Algebra
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Associative Rings and Algebras
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Group theory
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Group Theory and Generalizations
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Mathematics
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Authors:
Lee, Gregory T.
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Corporate Authors:
SpringerLink (Online service)
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Series:
Algebra and Applications
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Classification:
512.46
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512.46 (DDC 23)
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