naa a22 4500 510782620 CHVBK 20180411083252.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1007/s11856-012-0135-8 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0135-8 Multiple commutator formulas [Elektronische Daten] [Roozbeh Hazrat, Zuhong Zhang] Let A be a quasi-finite R-algebra (i.e., a direct limit of module finite algebras) with identity. Let I i , i = 0, ...,m, be two-sided ideals of A, GL n (A, I i ) be the principal congruence subgroup of level I i in GL n (A) and E n (A, I i ) be the relative elementary subgroup of level I i . We prove the multiple commutator formula $$\left[ {{E_n}(A,{I_0}),{\rm{G}}{{\rm{L}}_n}(A,{I_1}),{\rm{G}}{{\rm{L}}_n}(A,{I_2}), \ldots ,{\rm{G}}{{\rm{L}}_n}(A,{I_m})} \right] = \left[ {{E_n}(A,{I_0}),{E_n}(A,{I_1}),{E_n}(A,{I_2}), \ldots ,{E_n}(A,{I_m})} \right],$$ , which is a broad generalization of the standard commutator formulas. This result contains all the published results on commutator formulas over commutative rings and answers a problem posed by A. Stepanov and N. Vavilov. Hebrew University Magnes Press, 2013 Hazrat Roozbeh Department of Pure Mathematics, Queen's University, BT7 1NN, Belfast, UK aut Zhang Zuhong Department of Mathematics, Beijing Institute of Technology, 100081, Beijing, People's Republic of China aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/1(2013-06-01), 481-505 0021-2172 195:1<481 2013 195 11856 https://doi.org/10.1007/s11856-012-0135-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0135-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hazrat Roozbeh Department of Pure Mathematics, Queen's University, BT7 1NN, Belfast, UK aut NATIONALLICENCE 700 1- Zhang Zuhong Department of Mathematics, Beijing Institute of Technology, 100081, Beijing, People's Republic of China aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/1(2013-06-01), 481-505 0021-2172 195:1<481 2013 195 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer