Answer to Question #351028 in Abstract Algebra for Fed

Question #351028

3.9 Show that the commutative ring D is an integral domain if

and only if for a, b, c ∈ D with a #= 0 the relation ab = ac implies that

b = c.


1
Expert's answer
2022-06-22T16:41:40-0400

ab= ac"\\implies" ab-ac= 0

"\\implies" a(b-c)=0

"\\implies" a=0 or b-c=0

"\\implies" b-c=0 a≠0 "\\implies" b=c



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS