Crossword Genius

Non-intellectual's punch and argument after book is put down (7)

Ross

I believe the answer is:

lowbrow

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

'non-intellectual's' is the definition.
(I've seen this before)

'punch and argument after book is put down' is the wordplay.
I cannot really understand how this works, but
'argument' could be 'row' (to row is to argue) and 'row' is present in the answer.
'book' could be 'b' (abbreviation for book) and 'b' is located in the answer.
'down' could be 'low' (associated in meaning) and 'low' is found in the answer.
No letters remain.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for lowbrow that I've seen before include "Unintellectual" , "Uncultured (person)" , "(Person) uninterested in intellectual pursuits" , "Anti-intellectual" , "Non-intellectual person - observe forehead" .)

I've seen this clue in The Independent.
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