List questions from algebras

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Why $\textbf{Mon}(\textbf{Alg},\otimes_{\mathbb{k}},\mathbb{k}) = \textbf{CAlg}$?

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Prove that $\mathbb K[x] \times \mathbb K[y] \rightarrow \mathbb K[x,y] \,$ induces an isomorphism of $\mathbb K$-algebras.

Published on 21 Dec 2020 - 13:42

List Question

$M_n(k)\otimes_kB\cong M_n(B)$, where $k$ is a field, and $B$ is a $k$-algebra.

Difficulty with understanding and computing tensor products.

Module Isomorphisms of Maximal Orders

Additive function property on sigma algebra

Defining a "norm" on a nice $*$-algebra

Unitisation of an algebra: Is the norm $\text{max}\lbrace\|a\|_A,|\lambda|\rbrace$ submultiplicative?

Full finite abelian subcategories of $A\text{-mod}$

Under what conditions is a norm on an algebra equivalent to a submultiplicative norm?

Submodules of $k^n$ as $T_n(k)$-module

Semisimple algebra F[G] and restriction to subgroups

Why $\textbf{Mon}(\textbf{Alg},\otimes_{\mathbb{k}},\mathbb{k}) = \textbf{CAlg}$?

Quotients of algebras

Finding maximum of $x+y+z$

Isomorphism of algebras vs isomorphism of categories of representations

Prove that $\mathbb K[x] \times \mathbb K[y] \rightarrow \mathbb K[x,y] \,$ induces an isomorphism of $\mathbb K$-algebras.

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