Some identities on twisted group algebras

References

• Bateman, J. M. (1971). On the solvability of unit groups of group algebras. Trans. Amer. Math. Soc. 157:73–86. DOI: 10.1090/S0002-9947-1971-0276371-2.
   Web of Science ®Google Scholar
• Bateman, J. M., Coleman, D. B. (1968). Group algebras with nilpotent unit groups. Proc. Amer. Math. Soc. 19:448–449. DOI: 10.1090/S0002-9939-1968-0222186-6.
   Web of Science ®Google Scholar
• Bien, M. H., Kiani, D., Ramezan-Nassab, M. (2016). Some skew linear groups satisfying generalized group identities. Commun. Algebra 44:2362–2367. DOI: 10.1080/00927872.2015.1044109.
   Web of Science ®Google Scholar
• Billig, Y., Riley, D., Tasic, V. (1997). Nonmatrix varieties and nil-generated algebras whose units satisfy a group identity. J. Algebra 190:241–252. DOI: 10.1006/jabr.1996.6892.
   Web of Science ®Google Scholar
• Bovdi, A., Grishkov, A. (2008). Lie properties of crossed products. J. Algebra 320:3447–3460. DOI: 10.1016/j.jalgebra.2008.07.005.
   Web of Science ®Google Scholar
• Bovdi, A. (2005). Group algebras with a solvable group of units. Commun. Algebra 33:3725–3738. DOI: 10.1080/00927870500243213.
   Web of Science ®Google Scholar
• Bovdi, A., Khripta, I. I. (1977). Group algebras of periodic groups with solvable multiplicative group (Russian). Mat. Zametki 22:421–432; English translation in Math. Notes 22:725–731.
   Google Scholar
• Giambruno, A., Jespers, E., Valenti, A. (1994). Group identities on units of rings. Arch. Math. 63:291–296. DOI: 10.1007/BF01189563.
   Web of Science ®Google Scholar
• Golubchik, I. Z., Mikhalev, A. V. (1982). Generalized group identities in the classical groups. Zap. Nauch. Semin. LOMI AN SSSR. 114:96–119.
   Google Scholar
• Goncalves, J. Z. (1984). Free groups in subnormal subgroups and the residual nilpotence of the group of units of group rings. Can. Math. Bull. 27:365–370.
   Web of Science ®Google Scholar
• Gupta, N., Levin, E. (1983). On the Lie ideals of a ring. J. Algebra 81:225–231. DOI: 10.1016/0021-8693(83)90217-X.
   Web of Science ®Google Scholar
• Jespers, E., Riley, D., Siciliano, S. (2008). Group identities on the units of algebraic algebras with applications to restricted enveloping algebras. J. Algebra 319:4008–4017. DOI: 10.1016/j.jalgebra.2008.02.024.
   Web of Science ®Google Scholar
• Kezlan, T. P. (1965). Some rings with nil commutator ideals. Michigan Math. J. 12:105–111. DOI: 10.1307/mmj/1028999250.
   Web of Science ®Google Scholar
• Khripta, I. I. (1972). The nilpotence of the multiplicative group of a group ring (Russian). Mat. Zametki 11:191–200; English translation in Math. Notes 11:119–124.
   Google Scholar
• Lam, T. Y. (2001). A First Course in Noncommutative Rings, 2nd ed. New York: Springer-Verlag.
   Google Scholar
• Lee, G. T. (2010). Group Identities on Units and Symmetric Units of Group Rings. London: Springer.
   Google Scholar
• Liu, C.-H. (2002). On units of twisted group algebras. J. Algebra 250:271–282. DOI: 10.1006/jabr.2001.9088.
   Web of Science ®Google Scholar
• Liu, C.-H. (2000). Some properties on rings with units satisfying a group identity. J. Algebra 232:226–235. DOI: 10.1006/jabr.2000.8397.
   Web of Science ®Google Scholar
• Liu, C.-H., Passman, D. S. (1999). Group algebras with units satisfying a group identity II. Proc. Amer. Math. Soc. 127:337–341. DOI: 10.1090/S0002-9939-99-04684-5.
   Web of Science ®Google Scholar
• Liu, C.-H. (1999). Group algebras with units satisfying a group identity. Proc. Amer. Math. Soc. 127:327–336. DOI: 10.1090/S0002-9939-99-04744-9.
   Web of Science ®Google Scholar
• Passman, D. S. (2001). Twisted group algebras satisfying a generalized polynomial identity. Commun. Algebra 29:3683–3710. DOI: 10.1081/AGB-100105967.
   Web of Science ®Google Scholar
• Passman, D. S. (2001). Trace methods in twisted group algebras. Proc. Amer. Math. Soc. 129:943–946. DOI: 10.1090/S0002-9939-00-05613-6.
   Web of Science ®Google Scholar
• Passman, D. S. (1997). Group algebras whose units satisfy a group identity, II. Proc. Amer. Math. Soc. 125:657–662. DOI: 10.1090/S0002-9939-97-04024-0.
   Web of Science ®Google Scholar
• Passman, D. S. (1989). Infinite Crossed Products. New York: Academic Press.
   Google Scholar
• Passman, D. S. (1977). The Algebraic Structure of Group Rings. New York: Wiley.
   Google Scholar
• Passman, D. S. (1971). Group rings satisfying a polynomial identity, II. Pacific J. Math. 39:425–438. DOI: 10.2140/pjm.1971.39.425.
   Web of Science ®Google Scholar
• Ramezan-Nassab, M., Bien, M. H. (2020). Locally solvable unit group of crossed products. Commun. Algebra 48:5247–5253. DOI: 10.1080/00927872.2020.1784911.
   Web of Science ®Google Scholar
• Ramezan-Nassab, M. (2016). Group algebras with locally nilpotent unit groups. Commun. Algebra 44:604–612. DOI: 10.1080/00927872.2014.982817.
   Web of Science ®Google Scholar
• Riley, D. M., Wilson, M. C. (1999). Group algebras and enveloping algebras with nonmatrix and semigroup identities. Commun. Algebra 27:3545–3556. DOI: 10.1080/00927879908826645.
   Web of Science ®Google Scholar
• Rowen, L. H. (1980). Polynomial Identities in Ring Theory. New York: Academic Press.
   Google Scholar
• Sehgal, S. K. (1978). Topics in Group Rings. New York: Dekker.
   Google Scholar
• Tomanov, G. M. (1985). Generalized group identities in linear groups. Math. Sb. 51:33–46. DOI: 10.1070/SM1985v051n01ABEH002845.
   Google Scholar