https://scholars.lib.ntu.edu.tw/handle/123456789/606440
標題: | Additive subgroups generated by noncommutative polynomials | 作者: | Lee T.-K. TSIU-KWEN LEE |
關鍵字: | Higher commutator;Lie ideal;Maximal ideal;Noncommutative polynomial;PI-algebra;Simple algebra;Standard polynomial | 公開日期: | 2021 | 來源出版物: | Monatshefte fur Mathematik | 摘要: | Let R be an algebra. Given a noncommutative polynomial f, let f(R) stand for the additive subgroup of R generated by the image of f. For a unital or an affine algebra R, Sk(R) is completely determined for any standard polynomial Sk when R is generated by Sk(R) as an ideal. Motivated by Bre?ar’s paper [Adv. Math. 374 (2020), 107346, 21 pp] and Robert’s paper [J. Oper. Theory 75 (2016), 387–408], under certain conditions we also prove that f(R) is equal to either [R,?R] or the whole ring R. We obtain these results by studying the structure of Lie ideals L of a ring R whenever R is generated by [R,?L] as an ideal. ? 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature. |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85119342081&doi=10.1007%2fs00605-021-01644-3&partnerID=40&md5=3994a0862cf545ed291004d14b65bc17 https://scholars.lib.ntu.edu.tw/handle/123456789/606440 |
ISSN: | 00269255 | DOI: | 10.1007/s00605-021-01644-3 |
顯示於: | 數學系 |
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