A true relative of Suslin’s normality theorem

Abstract

We prove a normality theorem for the “true” elementary subgroups of ${\mathrm{SL}}_n(A)$ defined by the ideals of a commutative unital ring A. Our result is an analogue of a normality theorem, due to Suslin, for the standard elementary subgroups, and it greatly generalizes a theorem of Mennicke.