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Combined display of all available logs of ProofWiki. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).
- 19:53, 5 November 2023 12AbBa talk contribs created page Definition talk:Ring of Integers of Number Field (Created page with "Indeed, the Ring of Integers is usually defined for algebraic number fields. This is what Neukrich uses. You can do it for all number fields, but nobody cares about the ring of integers of Q(π)... ~~~~")
- 07:49, 5 November 2023 12AbBa talk contribs created page Definition:Free Abelian Group (Created page with "== Definition == Let $G$ be an abelian group. $G$ is a '''free abelian group''' if and only if it has an integral basis. That is, $G$ is a '''free abelian group''' if and only if the $\mathbb Z$-module associated with $G$ is a free $\mathbb Z$-module.")
- 07:41, 5 November 2023 12AbBa talk contribs created page Definition:Integral Basis (Created page with "== Definition == Let $(G,+)$ be an abelian group. Let $(G,+,\circ)$ be the $\mathbb Z$-module associated with $G$. An '''integral basis''' of $G$ is a basis of $G$ over $\mathbb Z$.")
- 05:54, 5 November 2023 12AbBa talk contribs created page Ring of Integers of Number Field is Free Z-Module (Created page with "== Theorem == Let $K$ be an algebraic number field. Let $\OO_K$ be its ring of integers. Then $\OO_K$ is a free $\mathbb Z$-module. === Dimension === The dimension of $\OO_K$ as a free $\mathbb Z$-module is equal to $[K:\mathbb Q]$. == Proof == {{proof wanted}} Category:Alge...")
- 05:14, 5 November 2023 12AbBa talk contribs created page Definition:Complex Embedding (Created page with "==Definition== Let $K$ be a subfield of $\mathbb C$. A '''complex embedding''' of $K$ is an embedding of $K$ into $\mathbb C$. That is, a '''complex embedding''' is an (injective) field homomorphism $\sigma:K\to\mathbb C$. ==Sources== {{Planetmath|title = real and complex embeddings|url = realandcomplexembeddings}}")
- 05:07, 5 November 2023 12AbBa talk contribs created page Definition:Real Embedding (Created page with "==Definition== Let $K$ be a subfield of $\mathbb C$. A '''real embedding''' of $K$ is an embedding of $K$ into $\mathbb R$. That is, a '''real embedding''' is an (Definition:Injective) field homomorphism $\sigma:K\to\mathbb R$. ==Sources== {{Planetmath|title = real and complex embeddings|url = realandcomplexembeddings}}")
- 04:26, 5 November 2023 12AbBa talk contribs created page Definition talk:Field Homomorphism (Created page with "I propose to change the definition Field Homomorphism to preserve multiplicative identity. Fields are unital rings, so it seems strange to not force a field homomorphism to be a unital ring homomorphism. Under this definition, there is an annoying edge case of the trivial homomorphism (all others are injective), which doesn't behave well and nobody cares about anyway... If nobody responds within a few days I will change the definition and related theorems. ~~~~")