Abstract
ABSTRACTWe 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 , the set of all matrices over a field , 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.
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