I am currently self-reading the book 'Monomial Ideals' by Herzog-Hibi.
In lemma 1.3.5 of that book what is '$ P_j R_{p_i}$'? I know what $R_{p_i}$ is. It is the localization at $p_i$. But I am confused about '$P_j R_{p_i}$'.
Secondly in the proposition 1.3.7 what does the line ' f is regular on S/Q ' mean.
Thank you for your help! 
2026-03-25 23:08:36.1774480116
Minimal prime ideals and associated prime ideals
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