August 2008
Qualifying Examination
Algebra Part
There are only 6 questions. Do them all.
1. Let A be a nite abelian group. Prove that A is not a projective Z-module
and also that it is not an injectiv
(Topics for qualifying exam in algebra) 731 SYLLABUS
I. Set-up (over rings with unity, including noncommutative)
Modules and Homomorphism Theorems
Direct Sums and Products, Free Modules
(including Uni
Algebra Part of Qualifying Examination, August 23, 2010
Instructions: Do all questions, justify your answers with the necessary proofs. All
rings are associative (not necessarily commutative) with ide
Q ualifying Exam - January 2009
Algebra Part
Instructions: C omplete as m any q uestions a s possible. Answers should be justified with
the necessary proofs. All rings are a ssumed to be n oncom mutat
Algebra P art o f Qualifying Examination, A ugust 25, 2009
Instructions: Do all questions, justify your answers with the necessary proofs.
All rings are associative (not necessarily commutative) with
Qualifying Examination
January 10, 2008
Algebra Part
Please do all ve questions.
Problem #5 is worth twice as much as each of the others
We will always assume that rings have an identity element and