Crossword Genius

In place of learning, rotter’s in A&E with me! (7)

Ross

I believe the answer is:

academe

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'in place of learning' is the definition.
I can't judge whether this definition defines the answer.

'rotter's in ae with me' is the wordplay.
'rotter' becomes 'cad' (a cad is a dishonourable person).
'in' indicates putting letters inside.
'with' means one lot of letters go next to another.
'cad' going within 'ae' is 'acade'.
'acade'+'me'='ACADEME'

Can you help me to learn more?

(Other definitions for academe that I've seen before include "college" , "The world of scholars" , "intellectual world" , "The world of teaching" , "universities" .)

I've seen this clue in The Times.
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