Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with ra.rings-and-algebras
Search options questions only
not deleted
user 2530
Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
9
votes
1
answer
477
views
Is a biideal of a Noetherian Hopf algebra automatically Hopf?
Let $H$ be a Hopf algebra over a field $k$, and $I$ be a biideal of $H$. I am looking for conditions that guarantee that $I$ is a Hopf ideal (that means $S\left(I\right)\subseteq I$).
One condition t …
- 33.8k
8
votes
2
answers
538
views
Artin Jacobson-semisimple rings are semisimple. Constructively, too?
Notation. When I say "ring", I mean "ring with unity" (not necessarily commutative).
Definition. A ring $R$ is said to be left-Artinian if for every sequence $I_0\supseteq I_1\supseteq I_2\supseteq I …
- 33.8k
1
vote
1
answer
171
views
Linear functional kills all primitives of a connected filtered coalgebra => it lies in m^2?
Let $C$ be a connected filtered coalgebra over a field $k$. Maybe $k$ has characteristic $0$ (though I don't know where this can be of use). Let $1$ denote the unique element of $C_0$ mapping to $1\in …
- 33.8k
9
votes
2
answers
3k
views
Jacobson radical = intersection of all maximal two-sided ideals
I'm embarassed to ask this question, but the literature on noncommutative rings seems to give this a berth as if it was absolutely trivial and not worth discussing, and I can't prove it, so all I can …
- 33.8k
9
votes
2
answers
618
views
Is there any transitivity for separable algebras?
If $R$ is a commutative ring (with $1$), then an $R$-algebra $A$ is said to be separable if $A$ is projective as an $A$-$A$-bimodule. (The notion of an "$A$-$A$-bimodule" includes the requirement that …
- 33.8k
3
votes
2
answers
343
views
Pseudo-idempotent matrix generating a free module
Let $R$ be a commutative ring with $1$. Let $n$ and $k$ be nonnegative integers, and let $A\in\mathrm{M}_n\left(R\right)$ be a matrix such that $A\cdot R^n\cong R^k$ as $R$-modules. Assume that $A^2=\ …
- 33.8k
6
votes
2
answers
800
views
No more absolute simples than $p$-regular conjucacy classes: elementary proof?
I am wondering whether anyone knows an elementary (no number fields, no Brauer characters; ideally, not even passing to algebraic extensions) proof of the following fact:
Let $G$ be a finite group. L …
- 33.8k
6
votes
2
answers
373
views
Is the Cartan matrix of a finite-dimensional (Hopf) algebra invertible over the rationals?
This is probably well-known to representation theorists, but this doesn't imply being well-known to me.
Let $k$ be a field, and let $A$ be a $k$-algebra that is finite-dimensional as a $k$-vector spa …
- 33.8k
9
votes
1
answer
1k
views
First-order UFD (factorial ring) condition / pre-Schreier rings
All rings in this post are commutative and with $1$.
Everyone knows the definition of a factorial ring, a. k. a. unique factorization domain (UFD). I have been wondering about some variations regardi …
- 33.8k
5
votes
0
answers
246
views
Injectivity criterion for surjective coalgebra maps: does it hold in full generality?
Let $\mathbf{k}$ be a commutative ring.
Let $C$ be a filtered $\mathbf{k}$-coalgebra. This means a $\mathbf{k}$-coalgebra equipped with an increasing $\mathbf{k}$-module filtration $C^0 \subseteq C^1 …
- 33.8k
4
votes
2
answers
655
views
Central idempotents from characters in Frobenius algebras (generalizing Lusztig arXiv:math/0...
$\newcommand{\refone}{\textbf{(1)}} \newcommand{\Hom}{\operatorname{Hom}} \newcommand{\tr}{\operatorname{Tr}} \newcommand{\kk}{\mathbf{k}}$ Let $\kk$ be a field. Let $A$ be a $\kk$-algebra which is fi …
- 33.8k
11
votes
1
answer
1k
views
PBW theorem over a Q-algebra, without freeness or flatness
Let $k$ be a commutative ring with $1$. Let $L$ be a $k$-Lie algebra, which is not necessarily free as a $k$-module. Let $S\left(L\right)$ denote the symmetric algebra of $L$ (over $k$), constructed a …
- 33.8k
14
votes
1
answer
540
views
Is the discriminant of a free (as a module) $R$-algebra always congruent to a square modulo 4?
Let $R$ be a commutative ring. Let $A$ be an $R$-algebra (i.e., an $R$-module
equipped with an $R$-bilinear multiplication map that turns $A$ into a unital
ring). We do not require $A$ to be commutat …
- 33.8k
3
votes
0
answers
135
views
Composition of Frobenius $n$-homomorphisms, characteristic-free?
This question is, as so often, a crossbreed of curiosity and laziness. The
former has led me to an interesting, but somewhat unsatisfactory paper by
Khudaverdian and Voronov
(arXiv:2002.02395v2) and, …
- 33.8k
5
votes
0
answers
79
views
Embedding the Mészáros subdivision algebra in an Orlik-Terao localization
The following is an open question (Question 4.1) from my paper $t$-Unique
Reductions for Mészáros's Subdivision Algebra (published version in
SIGMA 2018, and slightly updated preprint
version with mor …
- 33.8k