Timeline for If $H$ is essentially equimorphic to $K$, then is $H$ atomic only if so is $K$?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Apr 4, 2017 at 22:34 | vote | accept | Salvo Tringali | ||
| Apr 3, 2017 at 17:30 | comment | added | Salvo Tringali | For the record, the converse is true under mild assumptions, that are often met in applications (where K is typically a monoid of zero-sum sequences over an abelian group $G$ with support in a set $G_0\subseteq G$): (i) if $K$ is reduced (i.e., the only unit of $K$ is the identity) and atomic; (ii) if $K$ is atomic and $\varphi$ is a weak transfer homomorphism (viz., an essentially surjective equimorphism with the additional property that $\varphi^{-1}(K^\times)\subseteq H^\times$). | |
| Apr 3, 2017 at 8:41 | history | edited | Salvo Tringali | CC BY-SA 3.0 |
confused March with April...
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| Apr 3, 2017 at 8:31 | history | edited | Salvo Tringali | CC BY-SA 3.0 |
fixed a mistake
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| Apr 1, 2017 at 21:30 | history | edited | Salvo Tringali | CC BY-SA 3.0 |
fixed one more mistake
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| Apr 1, 2017 at 19:03 | answer | added | Salvo Tringali | timeline score: 1 | |
| Apr 1, 2017 at 17:32 | history | edited | Salvo Tringali | CC BY-SA 3.0 |
fixed a mistake in the definition of the set of factorizations
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| Apr 1, 2017 at 17:30 | comment | added | Salvo Tringali | My fault, it's a mistake: I want $\mathscr{Z}_H(x) := \pi_H^{-1}(x) \cap \mathscr{F}^\ast(\mathcal A(H))$ for every $x \in H$. Besides that, I think I can prove that the answer is in the affirmative. I will post it later. | |
| Apr 1, 2017 at 17:13 | comment | added | Benjamin Steinberg | Since $\pi_H$ is defined in the free monoid on H why would $\pi_H^{-1}$ be contained in the free monoid on the atoms? | |
| Apr 1, 2017 at 11:55 | history | edited | Salvo Tringali | CC BY-SA 3.0 |
fixed a typo and a mistake in the definition of an atom
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| Apr 1, 2017 at 10:22 | history | edited | Salvo Tringali | CC BY-SA 3.0 |
added the definition of atom
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| Apr 1, 2017 at 10:04 | history | edited | Salvo Tringali | CC BY-SA 3.0 |
deleted 7 characters in body
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| Apr 1, 2017 at 9:58 | history | edited | Salvo Tringali | CC BY-SA 3.0 |
deleted 361 characters in body
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| Apr 1, 2017 at 9:52 | history | asked | Salvo Tringali | CC BY-SA 3.0 |