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



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