# Tagged Questions

Questions about rings satisfying the descending chain condition on ideals.

816 views

### Lengths over a local ring

Let $A$ be a noetherian domain, $\mathfrak{m}$ а maximal ideal, $s$ a non-zero element of $\mathfrak{m}$, $d= \dim A_\mathfrak{m}$. Is the following claim true? Claim: For any $\epsilon>0$, there ...
373 views

### A left Artinian ring that is also a right Noetherian ring [closed]

I am having trouble showing that a ring which is left Artinian and right Noetherian is right Artinian.
367 views

### Are there only finite many maximal left ideals for a left Artinian ring?

As in title. Are there only finite many maximal left ideals for a left Artinian ring?
568 views

### When is a local Artin C-algebra a subring of C[t]/t^n

Let $A$ be a local ring over $\mathbb{C}$, which moreover is a finite dimensional $\mathbb{C}$-vector space. When is $A$ a subring of $\mathbb{C}[t]/t^n$? What does the minimal ...
525 views

### local Artin algebras

Given a commutative Artin algebra $A$ over an algebraically closed field $k$ one has a decomposition $A=A_1\oplus\ldots\oplus A_n$ into local Artin subalgebras, see for example Atiyah-McDonald, ...
Let $f:X\rightarrow Y$ be a morphism of schemes over a field $k$. Can one check that $f$ is formally smooth using only Artin rings of the form $k^{\prime}\left[t\right]/t^{n}$, where $k^{\prime}$ is ...