Multiplicative group (original) (raw)
In mathematics and group theory, the term multiplicative group refers to one of the following concepts: * the group under multiplication of the invertible elements of a field, ring, or other structure for which one of its operations is referred to as multiplication. In the case of a field F, the group is (F ∖ {0}, •), where 0 refers to the zero element of F and the binary operation • is the field multiplication, * the algebraic torus GL(1)..
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| dbo:abstract | In mathematics and group theory, the term multiplicative group refers to one of the following concepts: * the group under multiplication of the invertible elements of a field, ring, or other structure for which one of its operations is referred to as multiplication. In the case of a field F, the group is (F ∖ {0}, •), where 0 refers to the zero element of F and the binary operation • is the field multiplication, * the algebraic torus GL(1).. (en) In matematica e nella teoria dei gruppi il termine gruppo moltiplicativo si riferisce, a seconda del contesto ad uno dei seguenti concetti: * qualsiasi gruppo la cui operazione binaria è scritta con notazione moltiplicativa (invece di essere scritta con la usata per i gruppi abeliani), * il sottogruppo rispetto alla moltiplicazione degli elementi invertibili di un campo, di un anello, o altra struttura che abbia la moltiplicazione tra le sue operazioni. Nel caso di un campo F il gruppo è {F - {0}, •}, dove 0 si riferisce all'elemento zero di F e l'operazione binaria • è la moltiplicazione del campo, * il . (it) jest pierścieniem z dzieleniem (algebrą łączną z dzieleniem) wtedy i tylko wtedy, gdy w przeciwnym razie zbiór jest mniejszy, np. * algebraiczny torus jest szczególnym przypadkiem ogólniejszego pojęcia snopa ale pojawia się często poza geometrią algebraiczną pod nazwą grupa multiplikatywna; jest rozmaitością grupową. * w geometrii algebraicznej: snop grup abelowych reprezentowany przez schemat grupowy grupą przekrojów tego snopa nad afinicznym zbiorem otwartym jest grupa homomorfizmów pierścieni ; ta grupa jest naturalnie izomorficzna z grupą homomorfizmowi odpowiada jednoznacznie element przy czym Sam schemat też jest nazywany grupą multiplikatywną. (pl) 数学と群論において、用語乗法群 (multiplicative group) は次の概念の1つを意味する： * 体、環、あるいはその演算の 1 つとして乗法をもつ他の構造の、可逆元が乗法の下でなす群。体 F の場合には、群は {F ∖ {0}, •} である、ただし 0 は F の零元であり二項演算 • は体の乗法である。 * GL(1). (ja) |
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| dbp:date | March 2015 (en) |
| dbp:reason | this is not defined in this article nor in the linked article (en) |
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| rdfs:comment | In mathematics and group theory, the term multiplicative group refers to one of the following concepts: * the group under multiplication of the invertible elements of a field, ring, or other structure for which one of its operations is referred to as multiplication. In the case of a field F, the group is (F ∖ {0}, •), where 0 refers to the zero element of F and the binary operation • is the field multiplication, * the algebraic torus GL(1).. (en) In matematica e nella teoria dei gruppi il termine gruppo moltiplicativo si riferisce, a seconda del contesto ad uno dei seguenti concetti: * qualsiasi gruppo la cui operazione binaria è scritta con notazione moltiplicativa (invece di essere scritta con la usata per i gruppi abeliani), * il sottogruppo rispetto alla moltiplicazione degli elementi invertibili di un campo, di un anello, o altra struttura che abbia la moltiplicazione tra le sue operazioni. Nel caso di un campo F il gruppo è {F - {0}, •}, dove 0 si riferisce all'elemento zero di F e l'operazione binaria • è la moltiplicazione del campo, * il . (it) 数学と群論において、用語乗法群 (multiplicative group) は次の概念の1つを意味する： * 体、環、あるいはその演算の 1 つとして乗法をもつ他の構造の、可逆元が乗法の下でなす群。体 F の場合には、群は {F ∖ {0}, •} である、ただし 0 は F の零元であり二項演算 • は体の乗法である。 * GL(1). (ja) jest pierścieniem z dzieleniem (algebrą łączną z dzieleniem) wtedy i tylko wtedy, gdy w przeciwnym razie zbiór jest mniejszy, np. * algebraiczny torus jest szczególnym przypadkiem ogólniejszego pojęcia snopa ale pojawia się często poza geometrią algebraiczną pod nazwą grupa multiplikatywna; jest rozmaitością grupową. * w geometrii algebraicznej: snop grup abelowych reprezentowany przez schemat grupowy grupą przekrojów tego snopa nad afinicznym zbiorem otwartym jest grupa homomorfizmów pierścieni ; ta grupa jest naturalnie izomorficzna z grupą homomorfizmowi odpowiada jednoznacznie element przy czym (pl) |
| rdfs:label | Gruppo moltiplicativo (it) 乗法群 (ja) Multiplicative group (en) Grupa multiplikatywna (pl) |
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