Reduction of a polynomial modulo

Question

I have a question about "reduction of a polynomial modulo ideal"

Namely in Reid's book 'Undergraduate Commutative Algebra' (on p. 22) there is a description of prime ideals in $ K[X,Y]$

'... where $p\in K[X]$... $g\in K[X,Y]$ a polynomial whose reduction modulo $p$ is an irreducible element $\bar{g}\in(K[X]/(p))[Y]$...'

And my question is what is precisely this 'reduction of a polynomial modulo $p$'?

Thank you very much in advance for any response.

Answer 1

Here is is simply the image of $g$ under the ring homomorphism $$K[X,Y]=K[X][Y]\to (K[X]/p)[Y].$$