Let A be a finite-dimensional algebra over the rational numbers. The Wedderburn-Maltsev theorem tates that A decomposes as a sum of a semisimple subring and the Jacobson radical of A. In this aper the authors study the consequences of the Wedderburn-Maltsev theorem for unit groups of classical orders in such an algebra. The authors call the subgroup of a group consisting of all elements with finitely many conjugates the finite conjugacy centre. A priori this need not be a central subgroup.
Dooms, A, Jespers, E & Juriaans, SO 2003, 'Units in Orders and Integral Semigroup Rings', Journal of Algebra, vol. 265, pp. 675-689.
Dooms, A., Jespers, E., & Juriaans, S. O. (2003). Units in Orders and Integral Semigroup Rings. Journal of Algebra, 265, 675-689.
@article{9cf5cf5947d44b52bff3b74f20b65275,
title = "Units in Orders and Integral Semigroup Rings",
abstract = "Let A be a finite-dimensional algebra over the rational numbers. The Wedderburn-Maltsev theorem tates that A decomposes as a sum of a semisimple subring and the Jacobson radical of A. In this aper the authors study the consequences of the Wedderburn-Maltsev theorem for unit groups of classical orders in such an algebra. The authors call the subgroup of a group consisting of all elements with finitely many conjugates the finite conjugacy centre. A priori this need not be a central subgroup.",
author = "Ann Dooms and Eric Jespers and Juriaans, {Stanley Orlando}",
note = "Journal of Algebra 265 (2) (2003), 675-689",
year = "2003",
month = may,
day = "28",
language = "English",
volume = "265",
pages = "675--689",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
}