On classification of special linear group over commutative rings

Abstract

In [2] and [3] we described the double coset decomposition for the modular group SLr+s (Z) with respect to the congruence subgroup Р r,s (m) for any positive integer m. In the present paper we obtain the double coset decomposition of SLr+s (R) with respect to Р r,s (I). Where R is a commutative ring with unioty 1, and I is a nonzero ideal in R such that R/I is the direct sum of local principal ideal rings; thus generalize the results obtained in [2] and [3].