Questions tagged [rngs]

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

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Can $\mathbf{Rng}$ be made into a pre-additive category?

Question: Can $\mathbf{Rng}$ be made into a pre-additive category? Rngs are just rings, without the requirement of an identity. Accordingly, we do not require rng homomorphisms to preserve the ...
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Formula for two sided principal ideal for a ring without unity

How to express, the two sided principal ideal of a ring without unity(Rng)? How to express, the two sided ideal of a ring $R$ generated by some subset $S\subseteq R$ where $R$ is ring without unity(...
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Looking for counterexamples (non-domains)

I stumbled upon this question Why doesn't $xa = x$ for all $x \in R$ imply that $a$ is the unit of $R$? and understood the given answers. But it got me thinking about a counterexample, and I was ...
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Semiring of classes of associates of a ring/rng

Let's call elements that generate the same principal ideal of a ring/rng associates. $[a]$ is the equivalence class of associates of an element $a$ of a ring/rng. Let $A = \{[a],[b], ...\}$ be the ...
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In a commutative ring $R$ if, for every $a\in R$, the smallest ideal containing $a$ is equal to $Ra$ then $R$ has identity?

Let $R$ be a commutative ring such that, for every $a\in R$, the smallest ideal containing $a$ is equal to $Ra$. Does $R$ have identity? I did this when $R$ has at least one non-zero divisor then it'...
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Non-unital ring $(2\mathbb{Z})[X]$ is not Noetherian

Let $R = 2\mathbb{Z}$. Then $R[x]$ is not a noetherian ring. I do not understand why this is so, because Hilbert's basis theorem says: If R Noetherian ring, then R[X] a is Noetherian ring (from wiki)....
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