Robbins algebra (original) (raw)
In abstract algebra, a Robbins algebra is an algebra containing a single binary operation, usually denoted by , and a single unary operation usually denoted by . These operations satisfy the following axioms: For all elements a, b, and c: 1. * Associativity: 2. * Commutativity: 3. * Robbins equation: For many years, it was conjectured, but unproven, that all Robbins algebras are Boolean algebras. This was proved in 1996, so the term "Robbins algebra" is now simply a synonym for "Boolean algebra".
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| dbo:abstract | In abstract algebra, a Robbins algebra is an algebra containing a single binary operation, usually denoted by , and a single unary operation usually denoted by . These operations satisfy the following axioms: For all elements a, b, and c: 1. * Associativity: 2. * Commutativity: 3. * Robbins equation: For many years, it was conjectured, but unproven, that all Robbins algebras are Boolean algebras. This was proved in 1996, so the term "Robbins algebra" is now simply a synonym for "Boolean algebra". (en) In algebra astratta, un'algebra di Robbins è un'algebra contenente un'unica operazione binaria, solitamente indicata da e un'unica operazione unaria solitamente indicata da . Queste operazioni soddisfano i seguenti assiomi: Per ogni elemento , e : 1. * associatività: 2. * commutatività: 3. * equazione di Robbins: Per molti anni fu congetturato, ma non dimostrato, che tutte le algebre di Robbins fossero algebre booleane. La congettura fu dimostrata nel 1996, quindi il termine "algebra di Robbins" può essere considerato sinonimo di "algebra di Boole". (it) Een Robbins-algebra is een algebra bestaande uit de verzameling { 0, 1 } en de logische operatoren (disjunctie, "of") en (negatie, "niet") en de volgende axioma's. Associativiteit: Commutativiteit: Axioma van Robbins: Elke booleaanse algebra is een Robbins-algebra maar of elke Robbins-algebra een booleaanse algebra is, was enige tijd onbekend. Het vermoeden van Robbins is dat deze axioma's equivalent zijn aan die van de booleaanse algebra. Het werd voor het eerst geformuleerd door . Het vermoeden werd in 1996 bewezen door met behulp van een . (nl) |
| dbo:wikiPageExternalLink | https://www.sciencedirect.com/science/article/pii/S0021869398974671 http://calculemus.org/MathUniversalis/4/6robbins.html http://math.colgate.edu/~amann/MA/robbins_complete.pdf |
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| rdfs:comment | In abstract algebra, a Robbins algebra is an algebra containing a single binary operation, usually denoted by , and a single unary operation usually denoted by . These operations satisfy the following axioms: For all elements a, b, and c: 1. * Associativity: 2. * Commutativity: 3. * Robbins equation: For many years, it was conjectured, but unproven, that all Robbins algebras are Boolean algebras. This was proved in 1996, so the term "Robbins algebra" is now simply a synonym for "Boolean algebra". (en) In algebra astratta, un'algebra di Robbins è un'algebra contenente un'unica operazione binaria, solitamente indicata da e un'unica operazione unaria solitamente indicata da . Queste operazioni soddisfano i seguenti assiomi: Per ogni elemento , e : 1. * associatività: 2. * commutatività: 3. * equazione di Robbins: Per molti anni fu congetturato, ma non dimostrato, che tutte le algebre di Robbins fossero algebre booleane. La congettura fu dimostrata nel 1996, quindi il termine "algebra di Robbins" può essere considerato sinonimo di "algebra di Boole". (it) Een Robbins-algebra is een algebra bestaande uit de verzameling { 0, 1 } en de logische operatoren (disjunctie, "of") en (negatie, "niet") en de volgende axioma's. Associativiteit: Commutativiteit: Axioma van Robbins: Elke booleaanse algebra is een Robbins-algebra maar of elke Robbins-algebra een booleaanse algebra is, was enige tijd onbekend. Het vermoeden van Robbins is dat deze axioma's equivalent zijn aan die van de booleaanse algebra. Het werd voor het eerst geformuleerd door . Het vermoeden werd in 1996 bewezen door met behulp van een . (nl) |
| rdfs:label | Algebra di Robbins (it) Robbins-algebra (nl) Robbins algebra (en) |
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