Let $R$ be a ring. Show that the set $A=\{x \in R:xy=yx \ \forall y\in R \}$ is a subring of $R$.
83100
Prove that the center of a ring is a subring.
151803
Prove that $R$ is commutative
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
69353
Show that a ring with only trivial right ideals is either a division ring or $|R|=p$ and $R^2=\{0\}$. Why would $R$ be finite?
30327
$\ker \phi = (x_1-a_1, ..., x_n-a_n)$ for a ring homomorphism $\phi: R[x_1, ..., x_n] \to R$
111104
Ring theory notation question
155445
What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$?
85961
Is the ring and semi-ring definition of algebra and set linked?
142863
Show that every ideal of the matrix ring $M_n(R)$ is of the form $M_n(I)$ where $I$ is an ideal of $R$
91962
In a ring $a*a=0$ then $a+a=0$
154495
Prove that a nontrivial subring of a ring that is a domain has the same identity
150986
For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
72507
Does $ab=1$ imply $ba=1$ in a ring?
157488
Proving that $k[x,y,z]/(xz - (y^2 + 1))$ is a normal ring.
105887
Ring and Subring with different Identities
137011
showing $\psi: R\to \mathbb C$ is ring isomorphism.
111114
Prove that an ideal in $k[x,y]$ is a prime ideal