Orders in rings based on the core-nilpotent decomposition
Janko Marovt · Linear and Multilinear Algebra · 2017
We study orders in unital rings that are derived from the core-nilpotent decomposition. The notion of the Drazin order, the C-N partial order and the S-minus partial order is extended from Mn(F), the set of all n×n matrices over a field F, to the set of all Drazin invertible elements in rings with identity. Properties of these orders are investigated, their characterizations are presented, and some known results are thus generalized.