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Results tagged with ra.rings-and-algebras
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user 7108
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.
0
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Skew fields inside quaternion division algebras
Yes, it is. This follows from the theory of central simple algebras. Here's another proof, possibly similar to Aakumadula's: let $D'=D\otimes \bar{k}\cong GL_2(\bar{k})$. If $D'$ has basis $1,a$ then …
- 7,952
5
votes
Free augmented algebras
The free functor is left adjoint to the forgetful functor. There are two forgetful functors from augmented algebras to vector spaces. One views the algebra as a vector space, the other removes the ide …
- 7,952
2
votes
1
answer
166
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Variant of co-Tor in a bimodule category
Say $\mathcal{C}$ is a strict monoidal abelian category and $A$ is a coalgebra object in $\mathcal{C}$, with left co-modules $M$ and right co-module $N$ (also in $\mathcal{C}$). Then we have a notion …
- 7,952
6
votes
Which is the correct universal enveloping algebra in positive characteristic?
This question popped up on the feed recently, and I wanted to add another, "brave new math"-style answer. Namely, the point of Lie algebras is that, in characteristic $0$, a Lie algebra (resp., an $L_ …
- 7,952
2
votes
0
answers
75
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Diagrammatic model for free product in monad infinity category
$\newcommand{\C}{\mathcal{C}}$ Suppose $M$ is a monad in an $\infty$-category $\C,$ and $A, B$ are two algebras over $M$. I'm willing to assume any reasonable "niceness" conditions on $\C$, $M$, etc: …
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