Which of the algebra isomorphisms hold?

Asked Aug 25 '15 at 18:10

Active Sep 19 '15 at 16:51

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Fix $m, n \ge 1$. Which of the algebra isomorphisms below hold?

$k\langle t_1, \dots, t_m\rangle \otimes_k k\langle s_1, \dots, s_n\rangle \cong k\langle t_1, \dots, t_m, s_1, \dots, s_n\rangle$
$k[ t_1, \dots, t_m] \otimes_k k[ s_1, \dots, s_n] \cong k[ t_1, \dots, t_m, s_1, \dots, s_n]$

edited Sep 17 '15 at 09:56

moonlight

asked Aug 25 '15 at 18:10

4

The square brackets mean commutative polynomials I assume. What do the angle brackets refer to? – Cheerful Parsnip Aug 25 '15 at 18:20
Also, is k a field and are the t_i and s_i all indeterminates? – Mose Wintner Aug 26 '15 at 03:10
1

The second isomorphism holds, the first is false. See this post. – Leo Dec 25 '15 at 14:04

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