120A: Homework 1
By: Michiel Kosters
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1. Completeness
We will check the following exercises from the book for completeness.
Section 1: 7, 18, 24, 33, 36, 37.
Sectio
120B: Homework 4
By: Michiel Kosters
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1. Book exercises
Complete the following book exercises:
Section 23: 4 ,11, 14, 16, 25, 34.
Section 26: 3, 28, 34.
2. Extra ex
.
Student ID:
Name:
MATH 120B, Winter 2013
Midterm, Feb 8, 2013
Show all work. If you detach any sheets from the exam, yoU-must put your name and ID number
on the detached sheets.
Question 1
Question
H OMEWORK 3
M ATH 120B (45040) W INTER 2012
Due Thursday, February 2nd at the beginning of discussion section.
1. a. Let R be a eld and let : R S be a ring homomorphism. Show that is either the zero
m
H OMEWORK 9
M ATH 120B (45040) W INTER 2012
Due Thursday, March 15th.
1 0
. (Remember, over a noncom1. Find all ideals of M22 (R) which contain the matrix
0 0
mutative ring, ideals must be closed unde
H OMEWORK 2
M ATH 120B (45040) W INTER 2012
Due Thursday, January 26th at the beginning of discussion section.
1. Let R denote a ring. An element r R is called nilpotent if there exists a positive int
H OMEWORK 8
M ATH 120B (45040) W INTER 2012
Due Thursday, March 8th.
1. Show that C[x]/(x2 ) and C[x]/(x) C[x]/(x) are isomorphic as C-vector spaces but not isomorphic as rings.
2. (This was on the rs
H OMEWORK 4
M ATH 120B (45040) W INTER 2012
Due Thursday, February 9th.
1. Let F be a eld and let be the function from F [x] to F which sends a polynomial an xn +
an1 xn1 + + a0 to the sum of its coef
H OMEWORK 7
M ATH 120B (45040) W INTER 2012
Due Thursday, March 1st.
1. Let S R denote a subset that is closed under addition and is closed under multiplication by
arbitrary elements in R. Must S be a