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  • https://math.libretexts.org/Bookshelves/Analysis/Tasty_Bits_of_Several_Complex_Variables_(Lebl)/06%3A_Complex_Analytic_Varieties/6.04%3A_Properties_of_the_Ring_of_Germs
    Given a commutative ring R, an ideal IR is a subset such that fgI whenever fR and gI and g+hI whenever g,hI. Show that if \(I \subsetneq ...Given a commutative ring R, an ideal IR is a subset such that fgI whenever fR and gI and g+hI whenever g,hI. Show that if I is a proper ideal (ideal such that I \not= \mathcal{O}_0), then I \subset \mathfrak{m}_p, that is \mathfrak{m}_p is a maximal ideal.

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