Cardinality of quotient ring $\mathbb{Z_6}[X]/(2X+4)$

abstract-algebra ring-theory ideals

Solution 1:

$\mathbb{Z_6}[X]/(2X+4)\simeq\mathbb{Z_2}[X]/(2X+4)\times\mathbb{Z_3}[X]/(2X+4)\simeq\mathbb{Z_2}[X]\times\mathbb{Z_3}$

Related

Showing that if $R$ is a commutative ring and $M$ an $R$-module, then $M \otimes_R (R/\mathfrak m) \cong M / \mathfrak m M$.
Prove that the limit definition of the exponential function implies its infinite series definition.
Proof that if $s_n \leq t_n$ for $n \geq N$, then $\liminf_{n \rightarrow \infty} s_n \leq \liminf_{n \rightarrow \infty} t_n$
When $L_p = L_q$?
Derangement formula for repeated permutation
A linear transform of a closed set is closed
Probability Problem on Divisibility of Sum by 3
Image of subgroup and Kernel of homomorphism form subgroups
Constructing the midpoint of a segment by compass
Metric space is totally bounded iff every sequence has Cauchy subsequence
Is $\int_{-\infty}^{\infty} \sin x \, \mathrm{dx}$ divergent or convergent?
Formal power series coefficient multiplication