In a ring $a \cdot a=a$ then $a+a=0$
91962
In a ring $a*a=0$ then $a+a=0$
126331
Associative ring with identity, inverses, divisors of zero and Artinianity
6128
If $a \cdot a = 1$ then $a = 1$ or $a = -1$
151806
Prove that $A^k = 0 $ iff $A^2 = 0$
16023
Are associates unit multiples in a commutative ring with $1$?
126672
Product of principal ideals: $(a)\cdot (b) = (a b)$
4486
If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$
18971
Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$
77764
Is "$a + 0i$" in every way equal to just "$a$"?
85913
R is commutative ring with identity & define $\circ$ on $R$ by for any $a,b \in R$ $a \circ b=a+b-ab$ Prove the following
74441
Zero divisors in matrix rings
121663
If $a$ is a zero divisor of $\mathbb{F}$, then does $a$ fail to have a multiplicative inverse?
45158
Centre of a matrix ring are $ \operatorname{diag}\{ a, a, ..., a \} $ with $ a\in Z(R) $
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
50908
Showing a Ring and an Ideal are equal
138337
On a ring $R$ where $x^2 = x$, we must have that $2x = 0$ and $R$ is commutative
106894
If a subring of a ring R has identity, does R also have the identity?