TY - JOUR
T1 - Multiple commutator formulas
AU - Hazrat, Roozbeh
AU - Zhang, Zuhong
PY - 2013/6
Y1 - 2013/6
N2 - 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, GLn(A, I i) be the principal congruence subgroup of level I i in GLn(A) and E n(A, I i) be the relative elementary subgroup of level I i. We prove the multiple commutator formula [En(A, I0), GLn(A, I1), GLn(A, I2), ... , GLn(A, Im)] = [En(A, I0), En(A, I1), En(A, I2), ... , En(A, Im)], 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.
AB - 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, GLn(A, I i) be the principal congruence subgroup of level I i in GLn(A) and E n(A, I i) be the relative elementary subgroup of level I i. We prove the multiple commutator formula [En(A, I0), GLn(A, I1), GLn(A, I2), ... , GLn(A, Im)] = [En(A, I0), En(A, I1), En(A, I2), ... , En(A, Im)], 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.
UR - http://www.scopus.com/inward/record.url?scp=84883817710&partnerID=8YFLogxK
U2 - 10.1007/s11856-012-0135-8
DO - 10.1007/s11856-012-0135-8
M3 - Article
AN - SCOPUS:84883817710
SN - 0021-2172
VL - 195
SP - 481
EP - 505
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -