Abstract Algebra - ideals and generators

  • #1

Homework Statement


a.) Let a=3-8i and b=2+3i. Find x,y ϵ Z[i] such that ax+by=1.
b.) Show explicitly that the ideal I=(85,1+13i) [itex]\subseteq[/itex] Z[i] is principle by exhibiting a generator.

Homework Equations


Given ideal: I=(85,1+13i) [itex]\subseteq[/itex] Z[i]
a=3-8i
b=2+3i

Honestly, I am beyond lost on this problem. Any help would be appreciated. Thanks!
 

Answers and Replies

  • #2
22,129
3,297
You should apply the division algorithm in a suitable way.
 

Related Threads on Abstract Algebra - ideals and generators

  • Last Post
Replies
3
Views
2K
Replies
0
Views
1K
Replies
5
Views
3K
Replies
1
Views
2K
  • Last Post
Replies
0
Views
883
  • Last Post
Replies
3
Views
6K
Replies
4
Views
2K
Replies
2
Views
2K
  • Last Post
Replies
1
Views
733
Top