Math 538 Commutative Algebra
Study Notes
Zhaoning Yang
January 4, 2014
1
Rudiments
2
Nakaymas Lemma
Denition 2.1. Let R be a ring, be an index set, and M be an R-module for each . we dene
(1)
(2)
M
=
Math 538 Commutative Algebra
Homework 4
Name: Zhaoning Yang
October 18, 2013
Problem 1 Let R be an integral domain and K(R) be its eld of fractions. We dene the normalization
of R to be the integral c
Math 538 Commutative Algebra
Homework 3
Name: Zhaoning Yang
October 4th, 2013
Problem 1 Suppose R is a ring and M, M are Rmodules. Prove that M M is at if and only if
M and M are individually at.
Solu
Math538 Commutative Algebra
Homework 2
Name: Zhaoning Yang
September 20, 2013
Problem 1 Suppose that W1 W2 are multiplicative sets in a ring R and M is an R-module. Show
1
1
1
that W2 (W1 M ) W2 M .
S
Math 538 Commutative Algebra
Homework 1
Name: Zhaoning Yang
September 4, 2013
Problem 1 Let R be a ring, if I, J, J are ideals in R, prove that I J J implies that either I J
or I J . If P is a prime i