Explain why ($\mathbb{Z}_6$, +, · ) is not a field, where + is addition modulo 6 and · is multiplication modulo 6.
76813
The ring $ℤ/nℤ$ is a field if and only if $n$ is prime
114152
Intermediate fields between $\mathbb{Z}_2 (\sqrt{x},\sqrt{y})$ and $\mathbb{Z}_2 (x,y)$
27704
Cardinality of quotient ring $\mathbb{Z_6}[X]/(2X+4)$
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
145561
About the additive group and the multiplicative group of a field
145140
Subfield of $\mathbb{Q}(\sqrt[n]{a})$
124455
Why multiplicative group $\mathbb{Z}_n^*$ is not cyclic for $n = 2^k$ and $k \ge 3$
76501
How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?
104300
Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.
108955
Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
153444
$\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
146470
Show $\mathbb{Z}[\sqrt{6}]$ is a Euclidean domain
126927
$\mathbb Q$ is not the direct product of two non-trivial groups.
45979
Deﬁne a new addition ⊕ and multiplication on Z by a⊕b = a + b−1 and ab = a + b−ab.
2458
Multiplicative group $(\mathbb R^*, ×)$ is group but $(\mathbb R, ×)$ is not group, why?
70861
$\mathbb P^n\times \mathbb P^m\not\cong \mathbb P^{m+n}$