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Rich women have no right to cook a noodle dish (4,4)

Ross

I believe the answer is:

chow mein

I'm a little stuck... Click here to teach me more about this clue!

'a noodle dish' is the definition.
'chow mein' can be an answer for 'dish' (chow mein is a kind of dish). I am not sure about the 'a noodle' bit.

'rich women have no right to cook' is the wordplay.
'have no' indicates named letters should be taken away.
'right' becomes 'r' (common abbreviation).
'to cook' is an anagram indicator.
'rich'+'women'='richwomen'
'richwomen' with 'r' taken away is 'ichwomen'.
'ichwomen' with letters rearranged gives 'CHOW-MEIN'.

Can you help me to learn more?

(Other definitions for chow mein that I've seen before include "Chinese-style dish of shredded meat(s) and fried noodles" , "Chop suey with noodles" , "Chinese noodle dish" , "Hi cowmen, fancy a Chinese dish?" , "'Chinese dish with fried noodles (4,4)'" .)

I've seen this clue in the Sydney Morning Herald.
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