If R is a commutative ring with identity that has exactly three ideals 0, I and R. Show that if a does not belong to the I then a is unit R.
96144
Every element outside the maximal ideal of a local ring is a unit
113512
Characteristic of nonzero commutative rings with unity
16023
Are associates unit multiples in a commutative ring with $1$?
103830
Each element of a ring is either a unit or a nilpotent element iff the ring has a unique prime ideal
40705
If $M$ is an $R$-module and $I\subseteq\mathrm{Ann}(M)$ an ideal, then $M$ has a structure of $R/I$-module
39049
Ring With Unity As a Direct Sum of Non-Zero Ideals
102316
why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$
115920
Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
32772
Proving units in a ring
41629
Structure of ideals in the product of two rings
89702
Let $R$ be a ring such that for all $a,b$ in $R$, $(a^2-a)b=b(a^2-a)$. Then $R$ is commutative
77198
Showing that the characteristic of a commutative ring R without zero divisors is 0 or prime
27766
Comaximal ideals in a commutative ring
150986
For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
19838
Prove that in general the set of the right zero divisors is different from the set of left zero divisors in a ring R
79535
Prove that $R$ is a commutative ring if $x^3=x$
14343
Every nonzero element in a finite ring is either a unit or a zero divisor