- #1
kathrynag
- 598
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Show that the direct sum of 2 nonzero rings is never an integral domain
I started by thinking about what a direct sum is
(a,b)(c,d)=(ac,bd)
(a,b)+(c,d)=(a+c,b+d)
We have an integral domain if ab=0 implies a=0 or b=0
I started by thinking about what a direct sum is
(a,b)(c,d)=(ac,bd)
(a,b)+(c,d)=(a+c,b+d)
We have an integral domain if ab=0 implies a=0 or b=0