Thank you for your replies.

For the application I had in mind it seems that 'floating-point' numbers 
are not suitable.

I was doing computations in 
sage: R = Zp(2,type='fixed-mod')
sage: M = Matrix(R,4,[0, 0, 1, 1, 2^19, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1])
sage: M.inverse().base_ring()
2-adic Field with floating precision 20
sage: (M.adjoint()*M.det().inverse_of_unit()).base_ring()
2-adic Ring of fixed modulus 2^20


Unfortunately the syntax is a little cumbersome. Is there a shortcut to 
this?
Invert a matrix without exending the base_ring (or throw an error)

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