Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
2709
How to show that every Boolean ring is commutative?
54916
Maximal ideal in commutative ring
66451
In a ring, how do we prove that a * 0 = 0?
138309
Ring whose all ideals are double-sided is commutative?
69649
If an ideal contains the multiplicative identity, then it is the whole ring
57031
Ring of fractions of $R$ is integral over $R$
53770
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
22544
Let R be a commutative ring, and let P be a prime ideal of R. Suppose that P has no nontrivial zero divisors in it. Show that R is an integral domain.
18971
Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
74559
$A$ and $B$ are ideals of a ring ${R}$ such that $A\cap B=\{0\}$. Prove that $st=0$ for every $s\in A, t\in B$.
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
144442
Let $R$ be a commutative unital ring. Is it true that the group of units of $R$ is not isomorphic with the additive group of $R$?
78626
Let $R$ be a commutative ring. If $R[X]$ is a principal ideal domain, then $R$ is a field.
122958
$R/I$ is commutative iff $rs-sr \in I$
106894
If a subring of a ring R has identity, does R also have the identity?
152102
Prove that for every complex $2$x$2$ matrix $A$, there exists a matrix $X$ such that $X^3=A^2$.