Proving that the ring $R$ of $2\times 2$ matrices over $\Bbb{Q}$ contains only two ideals: $(0)$ and $R$.
38817
Why is the ring of matrices over a field simple?
30714
A question on ring homomorphisms and maximal ideals.
80616
A ring with few invertible elements
133706
If R is a local ring, then its maximal left-ideal is a left and right ideal
130814
Quotient of semi-simple rings
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?
120181
The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
81296
If A and B are ideals of a ring, show that A + B = $\{a+b|a \in A, b \in B\}$ is an ideal
138826
To show that either $R$ is a field or $R$ is a finite ring with prime number of elements and $ab = 0$ for all $a,b \in R$.
149519
Prove that a Boolean ring is a Bezout ring .
107821
The ring of integers of $\mathbf{Q}[i]$
13606
Prove that $K$ is isomorphic to a subfield of the ring of $n\times n$ matrices over $F$.
29019
Ideals in direct product of rings
41629
Structure of ideals in the product of two rings
69352
Prove that $I= \{a+bi \in ℤ[i] : a≡b \pmod{2}\}$ is an maximal ideal of $ℤ[i]$.
69649
If an ideal contains the multiplicative identity, then it is the whole ring
26497
Take $\mathbb{R}$ as a vector space over $\mathbb{Q}$, then a basis for $\mathbb{R}$, then $|B|=2^{\aleph_0}$