Timeline for The existence of non-trivial homomorphisms $\prod_{n=1}^{\infty}\mathbb{Z}/\bigoplus_{n=1}^{\infty}\mathbb{Z}\to\mathbb{Z}/p\mathbb{Z}$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 29, 2014 at 8:10 | history | edited | Kevin Ventullo | CC BY-SA 3.0 |
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| Apr 28, 2014 at 12:48 | comment | added | Eric Wofsey | @SJR: The maximal ideals in that ring are naturally in bijection with ultrafilters on $\mathbb{N}$; your special case of Kevin's construction is the same as the ultrafilter construction. | |
| Apr 28, 2014 at 12:20 | comment | added | Sidney Raffer | Nice. Alternatively, we can think of the last displayed item as a ring $R$, every element of which satisfies the equation $x^p=x$. So if $I$ is any maximal ideal of $R$, then the elements of the field $R/I$ all satisfy the same equation, whence $R/I$ is the $p$-element field. | |
| Apr 28, 2014 at 12:04 | comment | added | Eric Wofsey | Note that this is a bit weaker than the construction with ultrafilters, because that construction actually can be lifted to a homomorphism $\prod_{n=1}^\infty \mathbb{Z} / \bigoplus_{n=1}^\infty \mathbb{Z}\to\widehat{\mathbb{Z}}$. | |
| Apr 28, 2014 at 7:50 | history | edited | Kevin Ventullo | CC BY-SA 3.0 |
added 12 characters in body
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| Apr 28, 2014 at 5:41 | history | answered | Kevin Ventullo | CC BY-SA 3.0 |