If $q(A) = 0$, then $q$ is divisible by the minimal polynomial of $A$
89473
Uniqueness of minimal polynomial: $f(x)$ divides $g(x)$
146980
Zero divisors of $\mathbb{Z}×\mathbb{Z}×\mathbb{Z}$
125096
Minimal polynomial of $\alpha=\sqrt 2e^\frac{2\pi i}{3}$
112045
A property of minimal prime ideal
41895
Show $\text{Hom}_{Ab}(A,\mathbb{Q}) = \{0\}$ for finite $A$
74777
Solvability and reducibility of a polynomial in a "chain" of finite fields
135385
$0 < a_0 \leq a_1 \leq \cdots \leq a_n$, show $ p_n(z) = a_0 z^n + a_1 z^{n-1} + \cdots + a_{n-1} z + a_n = 0$ has no root in $|z| < 1$
146715
A square matrix has the same minimal polynomial over its base field as it has over an extension field
97729
Show that a polynomial $f(x)$ over a field $k$ is irreducible if and only if the polynomial $f(x+1)$ is irreducible
103552
The minimal polynomial of a primitive $p^{m}$-th root of unity over $\mathbb{Q}_p$
153107
Does every connected component of $\{z : |P(z)|<1 \}$ contain a zero?
125604
Proof that $\mathbb{Z}$ has no zero divisors
155642
Understanding divison by monic polynomial in $R[x]$ where $R$ is an arbitrary ring
46265
Minimal polynomial of the operator $T:V\oplus W\to V\oplus W$
49121
Factorizing a polynomial $f$ in $A[x]$ (with $A$ commutative), where $f$ has a zero in its field of fractions
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
76640
Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$