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April 29th, 2014, 07:31 AM   #1
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Algebraic Geometry

Can anyone help me understand proposition 4.32.

http://www.jmilne.org/math/CourseNotes/AG.pdf
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June 8th, 2014, 11:38 AM   #2
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Math Focus: philosophy/found of math, metamath, logic, set/category/order/number theory, algebra, topology
Algebraic sets-coordinate ring of an algebraic set

Could someone help me with this please? In Milne's notes, chapter 2 Algebraic sets, paragraph Coordinate ring of an algebraic set, he says two polynomials $f, g \in k[X_1, \dots , X_n]$ define the same regular function on $V$ iff they define the same element of $k[V]$. Could someone please explain to me why is this so?
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