Royal property unequally divided between Regan and Cordelia (7)

I believe the answer is:

regalia

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'unequally divided between regan and cordelia' is the definition.
I can't judge whether this defines the answer.

'royal property' is the wordplay.
'royal' becomes 'regal' (synonyms).
'property' becomes 'ia' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'regal'+'ia'='REGALIA'

Can you help me to learn more?

(Other definitions for regalia that I've seen before include "Finery" , "Royal items" , "ceremonial gear" , "Crown, sceptre etc used at a coronation" , "Royal paraphernalia" .)

I've seen this clue in The Independent.

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