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Results tagged with ra.rings-and-algebras
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user 22131
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.
6
votes
Accepted
Free augmented algebras
For any choice of $\lambda_1,\dots,\lambda_n$ there is an isomorphism:
$$ k[X_1^{[\lambda_1]},\dots,X_n^{[\lambda_n]} ] \simeq k[Y_1^{[0]},\dots,Y_n^{[0]} ] $$
Which is given by $X_i \leftrightarro …
- 42.4k
11
votes
Strong Morita equivalence and representation theory
Let $A$ and $B$ be two $C^{*}$ algebras. Then the category of $*$-representation of $A$ on Hilbert space is equivalent to that of $B$ if and only if their enveloping von Neumann algebra are morita equ …
- 42.4k
15
votes
Accepted
What is the smallest variety of algebras containing all fields?
If I'm not mistaken, your answer is 'yes' : Let $M(A)$ be the set of maximal ideal of your commutative inverse ring $A$. Then you have a map :
$$A \rightarrow \prod_{\rho \in M(A) } A / \rho $$.
Eac …
- 42.4k