Let R be a finite commutative ring with unity. Prove that every non-zero element of R is either a zero-divisor or a unit. What happens if we drop the "finite" condition on R ?
Asked
Active
Viewed 238 times
0
-
3For the infinite case: Look at $\mathbb Z$, what are its zero divisors? Its units? – martini Dec 06 '13 at 21:32
-
I don't understand why this question have 3 votes down? +1 – Luis Valerin Dec 06 '13 at 21:38
-
Guys, look at the user's history. Pretty much we are doing the OPs homework... – LASV Dec 06 '13 at 21:39
-
@LuisValerin: See Luis's comment. – tomasz Dec 06 '13 at 21:40
-
Is true you are right. – Luis Valerin Dec 06 '13 at 21:43
-
sorry, I voted to delete my post. – Dustan Levenstein Dec 06 '13 at 21:45
-
@DustanLevenstein Don't apologise. Just check next time when it is a question that is just stated with no effort. Especially when it is a question that has probably been asked a trillion times =]. I did the same thing and learnt my lesson. – LASV Dec 06 '13 at 21:47
-
Why assume the ring is commutative? – dfeuer Dec 06 '13 at 21:50
-
Okay, apologies for apologizing. ;-) – Dustan Levenstein Dec 06 '13 at 21:53