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The current research investigates the core partial order for its further properties. We introduce a new property for matrices of index at most 1, namelyand is called as ‘the core-subtractivity’. This property then is used to explore relations between the powers and subtractivity properties of the core partial order. In particular, we prove thatis equivalent tounder the core-subtractivity property. We also examine some new conditions under which the core partial order is equivalent to the minus and diamond partial orders.

Some new results on the core partial order