# Questions tagged [rngs]

A rng is an associative ring without necessarily having a multiplicative identity (rng = ring - $i$dentity).

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### Why do not we exclude the zero ring from ring?

In the definition of field, we exclude $\{0\}$ by assuming $1\ne0$ (i.e. there must be at least two elements in the field). Therefore, it is not a field. However, in the case of ring definition, even ...
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### Show a ring is commutative if $r^2 = r + r$

The claim is that any ring $R$ in which for all $r \in R$ we have that $rr = r + r$, must be commutative. No assumptions are made about $R$ having multiplicative identity or being commutative. I was ...
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### In the ring $6\mathbb{Z}$ is $12\mathbb{Z}$ maximal ideal but not prime ideal?
I need to prove that in the ring $6\mathbb{Z} = \left\{x \in \mathbb{Z} \mid x = 6q, q \in \mathbb{Z}\right\}$ the subset $12\mathbb{Z}$ is a maximal ideal but not a prime ideal. I first wanted to ...