Timeline for Finite dimensional algebras over $\mathbb{Q}$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 3, 2020 at 14:07 | comment | added | Johannes Hahn | He meant "a direct product of matrix algebras", i.e. the skew fields $D_i$ in the Wedderburn decomposition $A/J \cong \prod_{i=1}^n D_i^{k_i\times k_i}$ are all equal to $K$ itself. This is always the case for algebraically closed $K$ (because the $D_i$ are of finite dimension over $K$) but not in general. | |
| Mar 3, 2020 at 13:37 | comment | added | 57Jimmy | Thanks a lot for your answer. With the sentence "$A/J$ is isomorphic to matrix algebras over $K$" do you mean that the quotient of $A$ by its Jacobson radical is isomorphic to some subalgebra of $M^{n \times n}(K)$ for some $n$? | |
| Mar 3, 2020 at 13:03 | vote | accept | 57Jimmy | ||
| Mar 3, 2020 at 12:31 | history | edited | Mare | CC BY-SA 4.0 |
deleted 5 characters in body
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| Mar 3, 2020 at 12:26 | history | answered | Mare | CC BY-SA 4.0 |