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Results tagged with ra.rings-and-algebras
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user 105816
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.
3
votes
Intuition for left Hopf-modules
Let me put my two cents in here too, as on MSE, together with Ré and Emily answers.
Directly concerning your question about the significance of the axiom involving $\rho$, consider the following: if $ …
- 718
4
votes
groupring morphisms and bialgebra
Your first claim is true even if you substitute $\mathbb{Z}$ with any integral domain $\Bbbk$. Actually what is true is that we have a bijection
$$\text{Bialg}_\Bbbk(\Bbbk[G],B)\cong\text{Mon}(G,\math …
- 718
8
votes
1
answer
811
views
A "concrete" example of a one-sided Hopf algebra
I came to know from the paper Left Hopf Algebras by Green, Nichols and Taft that one may consider a Hopf algebra whose antipode satisfies only the left (resp. right) antipode condition.
To be more pr …
- 718
2
votes
0
answers
114
views
Linear topologies on the finite dual of the polynomial algebra
Let $\Bbbk[X]$ be the polynomial algebra in one indeterminate over a field $\Bbbk$, endowed with the primitive-like bialgebra structure, i.e. $\Delta(X)=X\otimes1+1\otimes X$ and $\varepsilon(X)=0$.
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- 718