1,721,081 research outputs found
Are locally finite MV-algebras a variety?
No full textWe answer Mundici's problem number 3 (Mundici (2011) [37]): Is the category of locally finite MV-algebras equivalent to an equational class? We prove: 1. The category of locally finite MV-algebras is not equivalent to any finitary variety. 2. More is true: the category of locally finite MV-algebras is not equivalent to any finitely-sorted finitary quasi-variety. 3. The category of locally finite MV-algebras is equivalent to an infinitary variety; with operations of at most countable arity. 4. The category of locally finite MV-algebras is equivalent to a countably-sorted finitary variety. Our proofs rest upon the duality between locally finite MV-algebras and the category of “multisets” by R. Cignoli, E.J. Dubuc and D. Mundici, and known categorical characterisations of varieties and quasi-varieties. In fact, no knowledge of MV-algebras is needed, apart from the aforementioned duality
SEGNALAZIONE DI FLYSCH CRETACICO NELL'INCISIONE DEL VALLONE DEL SALTO TRA BRACIGLIANO E FORINO (CAMPANIA)
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RELATIVE IDEALS IN HOMOLOGICAL CATEGORIES WITH AN APPLICATION TO MV-ALGEBRAS
No full textLet A be a homological category and U: B → A be a faithful conservative right adjoint. We introduce the notion of relative ideal with respect to U and show that, under suitable conditions, any object of A can be seen as a relative ideal of some object in B. We then develop a case study: we first prove that the category of hoops is semi-abelian and that the category of MV-algebras is protomodular; then we apply our results to the forgetful functor from the category of MV-algebras to the category of Wajsberg hoops
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