Stack Exchange Network
Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Visit Stack Exchange
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.
Sign up to join this community
Anybody can ask a question
The best answers are voted up and rise to the top
I can prove that in finite commutative ring, non zero divisors are units. My question is if the reverse also true. I mean, units are non zero divisors? And what about the commutative infinite rings?
asked Dec 14, 2014 at 15:36
1,16211 gold badge88 silver badges1919 bronze badges
Units are always non zero-divisors. If $x$ is a unit, then $1=xy$ for some $y\in R$. Now, if $rx=0$, then $r=r(xy)=(rx)y=0$. So $x$ is not a zero-divisor.
answered Dec 14, 2014 at 15:41
10.2k44 gold badges3939 silver badges112112 bronze badges
You must log in to answer this question.