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vls/2603nrwcece.visuallibrary.netvdGroup identities on units and symmetric units of group ringsLee, Gregory T.1971-2024VerfasserauttextTextbookszXA-CHChamSpringer[2025]© 20252025Second editionmonographicengprintxx, 253 Seiten : Illustrationenohne Hilfsmittel zu benutzenBand"This book presents the 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. 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" [Verlag]Gregory T. LeeDie Erstausgabe erschien 2010 beim Springer-Verlag London LimitedGroup theoryGraph theoryConvex geometryDiscrete geometryProjective geometryGroup theory and generalizationsAssociative rings and algebrasGroup rings, Lie, Group identities, Involutions, Prime, Symmetric elements9783032046192978303204622299376385200806441HT031357318Online-Ausgabe (eBook)9783032046208Algebra and applications33(DE-605)HT01353991149HBZ_DUErda25121720260123145111.0154262701ger https://ce.visuallibrary.net//domainresource/static/graphics/connectors/viewerLogo.gif http://193.30.112.129:83/F/?func=find-c&ccl_term=ICS%3D154262701+X0001 https://ce.visuallibrary.net/id/1376025 https://ce.visuallibrary.net/i3f/v20/1376025/manifest https://ce.visuallibrary.net/proto_ftsearch/1376025