Higher algebraic $K$-groups and $\mathcal D$-split sequences

Details Higher algebraic $K$-groups and $\mathcal D$-split sequences Higher algebraic $K$-groups and $\mathcal D$-split sequences

2011-07-27

arxiv.org/abs/1107.5380v1

Mathematics

K-Theory and Homology

20 pages

Scientific paper

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 cover tiled orders, rings related to chains of Glaz-Vasconcelos ideals, and some other classes of rings. 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.

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