School of Mathematics
University of New South Wales
MATH3711: Higher Algebra (2007,S1)
Problem Sheet 6 1
1. Show that for any ring R, we have a ring isomorphism (Mn (R)[x]
Mn (R[x]) where of course, x is an indeterminate. Remark: I hope the
isomorphism is
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
June 2008
MATH3711
HIGHER ALGEBRA
(1) TIME ALLOWED 3 HOURS
(2) TOTAL NUMBER OF QUESTIONS 5
(3) ATTEMPT ALL QUESTIONS
(4) THE QUESTIONS ARE NOT OF EQUAL VALUE
(5) THIS PAPER MAY BE RETA
School of Mathematics
University of New South Wales
MATH3711: Higher Algebra (2007,S1)
Problem Sheet 3 1
1. Consider the subgroup R of C (you need not show it is a subgroup).
Describe geometrically, all the cosets of R in C. Identify the group
C/R i.e. sh
School of Mathematics
University of New South Wales
MATH3711: Higher Algebra (2007, S1)
Lecturer/Tutor: Daniel Chan
E-Mail: danielc@unsw.edu.au
Webpage: web.maths.unsw.edu.au/danielch
Oce: Red Centre (East Wing) Room 4104
Oce Phone No.: 9385 7084
Consulta
School of Mathematics
University of New South Wales
MATH3711: Higher Algebra (2007,S1)
Studying for this course 1
Mathematics went through quite a revolution around the turn of the 20th century.
In particular, axiomatics inltrated the mathematical paradig
School of Mathematics
University of New South Wales
MATH3711: Higher Algebra (2007,S1)
Problem Sheet 1 1
1. Given the following equation in a group x1 yxz 2 = 1, solve for y.
2. In any group G, show that (g 1 )1 = g for any g G. Show for any m, n Z that
g