Intereting Posts

Growth of $\Gamma(n+1,n)$ and $\operatorname{E}_{-n}(n)$
Trace of the power matrix is null
Is there possibly a largest prime number?
Conformal map between annulii
When is a function satisfying the Cauchy-Riemann equations holomorphic?
If a separately continuous function $f : ^2 \to \mathbb{R}$ vanishes on a dense set, must it vanish on the whole set?
Ellipse in polar coordinates
Math without infinity
What is the probability that the hand will contain the A K Q J 10 of spades.
Number of generators of the maximal ideals in polynomial rings over a field
Separability of Banach Spaces
Conjecture regarding integrals of the form $\int_0^\infty \frac{(\log{x})^n}{1+x^2}\,\mathrm{d}x$.
Presheaf image of a monomorphism of sheaves is a sheaf
Proof that a trigonometric function of a rational angle must be non-transcendental
Matrix Identity $(I-G_1G_2)^{-1}G_1=G_1(I-G_2G_1)^{-1}$?

I’m trying to prove that if $M$ is a simple module over $M_n(D)$ where $D$ is a division algebra, then $M\cong D^n$. I know that if $M$ is a simple module over $R$ then it is isomorphic to $Rv=\{rv|r\in R\}$ for all $v\in M$. I’m trying to find a $M_n(D)$ module isomorphism $f:M_n(D)v\rightarrow D^n$. I’ve been told to try the map that maps $Xv\mapsto Xe_1$, where $e_1$ is the column vector with 1st entry 1 and the rest 0. I can prove that this is a homomorphism but I’m stuck on the injectivity. Any help would be well appreciated!

- Why does the $n$-th power of a Jordan matrix involve the binomial coefficient?
- Smallest non-commutative ring with unity
- New discovery of the unconventional matrix representation for the quaternion $H_8$
- Prove that the Gaussian rationals is the field of fractions of the Gaussian integers
- Find the degree of the splitting field of $x^4 + 1$ over $\mathbb{Q}$
- Show that image of $res$ lies in $H^n(H,A)^{G/H}$
- Are intermediate rings of finitely generated ring extensions also finitely generated?
- Is there a division algorithm for any Euclidean Domain?
- free groups: $F_X\cong F_Y\Rightarrow|X|=|Y|$
- The uniqueness of a special maximal ideal factorization

The kernel of the map is itself a submodule of M. It must be trivial because M is simple.

- Coproduct of bounded distributive lattices given as lattices of subsets
- Any two norms equivalent on a finite dimensional norm linear space.
- Simplifying polynomials
- Higher homology group of Eilenberg-Maclane space is trivial
- Prove that two distinct number of the form $a^{2^{n}} + 1$ and $a^{2^{m}} + 1$ are relatively prime if $a$ is even and have $gcd=2$ if $a$ is odd
- What exactly IS a line integral?
- explicit formula for recurrence relation $a_{n+1}=2a_n+\frac{1}{a_n}$
- How do I show a particular polynomial has Galois group $Z_3$?
- Why do the first spikes in these plots point in opposite directions?
- A linear transformation satisfying $P^2 = P$
- Linear independency before and after Linear Transformation
- (Counting problem) very interesting Modular N algebraic eqs – for combinatorics-permutation experts
- Infinite Series $\sum\limits_{n=1}^\infty\left(\frac{H_n}n\right)^2$
- minimal surface of revolution when endpoints on x-axis?
- Distribution of $(XY)^Z$ for $(X,Y,Z)$ i.i.d. uniform on $(0,1)$