Questions tagged [rngs]

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

The term rng (pronounced "rung") is used to refer to an associative ring which does not necessarily have an identity element. (rng = ring - i​dentity). Use this tag if your question particularly is about certain conditions forcing the existence of identity, or a morphism preserving identity. Using this tag along with or will be appreciated.

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Characteristic of a non unital integral domain

Theorem: the characteristic of a non unital integral domain must be $0$ or a prime. Assume that $mn$ is the characteristic of a the integral domain for every $a$ in the integral domain we have $(mn)a^2=(ma)(na)=0$ then $ma$ or $na$ must be…
Arsh Gh
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Is the ring $m\mathbb{Z}$ isomorphic to the ring $n\mathbb{Z}$?

I came over a question in ring theory which I am not being able to proceed upon: When is the ring $m\mathbb{Z}$ isomorphic to the ring $n\mathbb{Z}$, where $m, n \in \mathbb{N}$? I know that to show isomorphism, I need to show that it is onto and…
Qwerty
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Prove that every maximal ideal of a commutative ring $R$ with $R^2=R$ is prime

Prove that every maximal ideal of a commutative ring $R$ (not assumed to have $1$) with $R^2=R$ is prime. If $M$ is a maximal ideal of $R$, I am trying to prove that for all $a,b,ab \in M$ implies $a\in M$ or $b \in M$, but I find it hard to…
Dong Han
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PRNG for compression

I'm trying to intuitively grasp information theory. You have a string of size X that contains a lot of information, say it's a movie. You have a string of size N << X which is going to be the algorithm of a PRNG function. And it has an internal…
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Ring of even integers considered as module over itself

I wonder, if the ring without unity $2\mathbb{Z}$, considered as a modul over itself, is a free modul. For a ring with unity, which is not the nullring the answer is clearly yes, because one can write every element r as r $\cdot$ 1, so {1} is a…
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Is there a ring without unity which can be expressed as a union of its three proper ideals?

Are there any rings without unity which can be expressed as a union of its three proper ideals?
Prince Kumar
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