All Questions
1,966 questions with no upvoted or accepted answers
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semigroup actions of groups on regular rooted trees
If $G$ is a group which has a semigroup action on a regular rooted tree via prefix-preserving, continuous transformations (I give the tree the path metric), what kinds of algebraic restrictions can we ...
- 125
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166
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Can the zero-degree part of $M_f \otimes_{S_f} N_f$ be identified with $M_{(f)} \otimes_{S_{(f)}} N_{(f)}$?
The isomorphism ${(M \otimes _ {S} N)} _ {f} = M _ {f} \otimes _ {S _ {f}} N _ {f}$ is well-known. Here, $S$ is a graded ring, and $M,N$ are graded $S$ modules.
Now, let $f$ be any homogeneous ...
- 945
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551
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sub ring of algebra over subfield
Let $k$ be a field and $k[a]$ an algebric extension.
If $A$ is a reduced commutative algebra over $k[a]$ and $B$ is a subring which is an algebra over $k$, then is the following true: if there exist ...
- 1
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237
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resolution of singular points on plane curves and base change
Let $k$ be a field and $C/k$ be an affine plane curve over $k$, namely $C = \mathrm{Spec}(A)$ for some $A = k[x,y]/(f(x,y))$, here $f(x,y) \in k[x,y]$ is an irreducible polynomial. Let $B$ be the ...
- 1,109
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544
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isomorphism between vector spaces and modules - Commutative Algebra
Hi, Let $M_i$ be A modules. Then we know that $Ass (\oplus M_i) = \bigcup Ass(M_i) $. We consider here isomorphisms between modules.
Now consider a stanley ...
- 287
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254
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What is Castelnuovo-Mumford regularity of this algebra?
Let $M=\mathbb{C}[f_1,f_2,\ldots,f_r]$ is finitely generated algebra, $f_i \in S:=\mathbb{C}[x_1,x_2,\ldots,x_n],$ $\deg(x_i)=1, 1<\deg(f_i)<99.$ Suppose that minimal free resolution of $...
- 301
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198
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why a reduced ring can be embedded into a sum of integral rings?
Hi,
the question is exactly
"why a reduced ring (commutative with 1) can be embedded into a sum of integral rings?"
Is this simply because in the normalization process we can have many irreducible ...
- 141
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197
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Existence of flat models of a smooth finite type algebra over $R((t))$
Let $k$ be a field, $R$ a $k$-algebra (of finite type if necessary),
$B$ an algebra of finite type over ring of the formal Laurent series $R((t))$, which is smooth.
Up to this generality, can one ...
- 51
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183
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Standard system of parameters and an example
Let $(R,m)$ be a local Noetherian ring. A system of parameters $\bf{x}$$:=x_{1}, \dots, x_{d}$ is a standard system of parameters if $(\bf{x})H^{i}_{m}(R/(x_{1}, \dots, x_{j}))=0$ holds for all non-...
- 113
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165
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Support sets along a ring homomorphism.
Let $(R,m)$ and $(S,n)$ be commutative noetherian local rings, and $f: R\rightarrow S$ be a local homomorphism (i.e., $f(m) \subseteq n$) with $S$ flat as $R$-module. If $M$ is a finite generated $R$-...
- 1,207
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votes
1
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213
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number of representations by sums of three squares (with coefficients)
There are formulas for counting the number of representations of a positive integer $N$ as a sum of three integer squares. What is a reference for
$$
\#\{(x,y,z)\in \mathbf{N}^3: 5^4 x^2+y^2+z^2=N\}
?$...
- 3,062
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votes
1
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349
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Log associahedra and log noncrossing partitions--raising ops and symmetric function theory for $A_n$ (references)
Where do the following three sets $[LA]$, $[ILA]$, and $[LN]$ of partition polynomials appear in the literature?
There are two sets of partition polynomials, not in the OEIS, that serve as the ...
- 10.5k
-1
votes
1
answer
555
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Noetherianity assumptions in Hartshorne's book
It seems that noetherian assumptions are not necessary in many results by Hartshorne, in his book "Algebraic Geometry". How much is this true? Could you please give examples?
- 1,422
-2
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1
answer
187
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behavior of multiplicity in exact sequences
Bruns-Herzog define multiplicity When the ring and module are not necessarily graded as $e(M)=e(gr_m(M))$, see B-H 4.6. I have two questions:
Question1. Many concepts in commutative algebra have ...
- 1,355
-2
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1
answer
151
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Quadratic extension and prime ideals
Let $B/A$ be a quadratic Galois extension between local domains. Define ${\mathrm{Gal}}(B/A) = \{e,\sigma\}$.
Choose two prime ideals ${\frak P}_1, {\frak P}_2$ of $B$ such that ${\frak P}_2 = {\...
- 781
-4
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1
answer
251
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What are the properties of 3-dimensional split-complex numbers?
I have often encountered claims that 3-dimensional numbers are impossible. But
it seems to me that $\mathbb{R}^3$ with Hadamard multiplication should in fact behave quite similar to split-complex ...
- 10.1k