Group Identities on Units and Symmetric Units of Group Rings
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....
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| Format: | Electronisk eBog |
| Sprog: | engelsk |
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Springer Nature Switzerland : Imprint: Springer,
2025.
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| Udgivelse: | 2nd ed. 2025. |
| Serier: | Algebra and Applications,
33 |
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| Online adgang: | https://doi.org/10.1007/978-3-032-04620-8 |
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| 100 | 1 | |a Lee, Gregory T. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Group Identities on Units and Symmetric Units of Group Rings |h [electronic resource] / |c by Gregory T. Lee. |
| 250 | |a 2nd ed. 2025. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2025. | |
| 300 | |a 1 online resource (XX, 253 p. 2 illus.). |b 1 illus. in color. | ||
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| 490 | 1 | |a Algebra and Applications, |x 2192-2950 ; |v 33 | |
| 505 | 0 | |a Group Identities on Units of Group Rings -- Group Identities on Symmetric Units -- Lie Identities on Symmetric Elements -- Nilpotence of and. | |
| 520 | |a 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. | ||
| 532 | 8 | |a Accessibility summary: This PDF has been created in accordance with the PDF/UA-1 standard to enhance accessibility, including screen reader support, described non-text content (images, graphs), bookmarks for easy navigation, keyboard-friendly links and forms and searchable, selectable text. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com. Please note that a more accessible version of this eBook is available as ePub. | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Group theory. | |
| 650 | 0 | |a Associative rings. | |
| 650 | 0 | |a Associative algebras. | |
| 650 | 1 | 4 | |a Group Theory and Generalizations. |
| 650 | 2 | 4 | |a Associative Rings and Algebras. |
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| 773 | 0 | |t Springer Nature eBook | |
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| 776 | 0 | 8 | |i Printed edition: |z 9783032046222 |
| 830 | 0 | |a Algebra and Applications, |x 2192-2950 ; |v 33 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-032-04620-8 |
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