Integral Jordan decomposition of matrices Original Research Article

We treat the question of Jordan decomposition for R-orders, where R is an integrally closed noetherian integral domain with perfect field of quotients K. We shall relate the existence of a Jordan decomposition for orders to Hochschild cohomology and derive local–global principles for Jordan decomposition. We treat the cases of orders contained in Mat(2, K) and of orders generated by a single element in detail, and develop a new procedure for computing the semisimple part of a matrix in Mat(n, K).