Prove a identity of a ring
75520
If $a^3 =a$ for all $a$ in a ring $R$, then $R$ is commutative.
87946
Proving that the unities of a ring form a group under multiplication
83255
Finding inverse in non-commutative ring
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
99567
Proving that an inverse ring homomorphism of an ideal is an ideal?
106008
Combinatorial Identity $(n-r) \binom{n+r-1}{r} \binom{n}{r} = n \binom{n+r-1}{2r} \binom{2r}{r}$
111824
Sum of nilpotent and element is a unit in ring?
156383
Proving a combinatorial identity without double counting
69012
How to directly prove every element in a ring with exactly three ideals is either a unit or a zero divisor?
134989
Prove that if the identity is written as the product of $r$ transpositions, then $r$ is an even number
5526
Prove that $ℤ[i]^*= \{1,-1,i,-i\}$
65224
Prove that if $a^2 = a$ for all elements of the ring $R$, then $R$ has characteristic 2. Is the converse of the statement true?
105913
Calculations in quotient rings
107900
A ring which has many distinct left inverses
34424
Determining ring of integers for $\mathbb{Q}[\sqrt{17}]$
107397
Algebraic proof for the identity $\sum_{k=0}^m(-1)^{m-k}{{n \choose {k}}}= {{n-1}\choose m}$
79535
Prove that $R$ is a commutative ring if $x^3=x$