Undergraduate Texts in Mathematics
Editors
F. W. Gehring
P. R. Halmos
Advisory Board
C. DePrima
I. Herstein
J. Kiefer
W. LeVeque
Tom M. Apostol
Introduction
to Analytic
Number Theory
Springer-Verlag
N
Selected Solutions to Artins Algebra, Second Ed.
Takumi Murayama
July 22, 2014
These solutions are the result of taking MAT323 Algebra in the Spring of 2012,
and also TA-ing for MAT346 Algebra II in t
Math 122, Solution Set No. 13
1
10.3.4
Let f (2) (x) Z[x]. Since x - 2 and 2 - x, we have f = 2xg(x) and so f (2x). Conversely, if
f (2x) Z[x] we have f = 2xg(x) f (2) (x). (2) (x) = (2x) Z[x].
2
10.3
Math 113 Homework 5
Solutions
due July 24, 2011
1. How many abelian groups are there of order 100? of order 16, 900?
Solution: 100 = 22 52 , so by the structure theorem for finite abelian
groups, ther