Higher algebraic K-groups and {\mathcal D}-split sequences

In this paper, we use ${\mathcal D}$ -split sequences and derived equivalences to provide formulas for calculation of higher algebraic K-groups (or mod-p K-groups) of certain matrix subrings which occur both in commutative algebra as the endomorphism rings of direct sums of Prüfer modules or of chains of Glaz–Vasconcelos ideals and in noncommutative geometry as an essential ingredient of the study of singularities of orders over surfaces. In our results, we do not assume any homological requirements on rings and ideals under investigation, and therefore extend sharply many existing results of this type in the algebraic K-theory literature to a more general context.