The Prime Spectrum of an MV‐Algebra

Belluce, L. P.; Nola, Antonio Di; Sessa, Salvatore

doi:10.1002/malq.19940400304

Cited by 26 publications

(15 citation statements)

References 30 publications

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“…Especially, [8, Theorem 5] 1 describes the l-groups correspondents of boolean algebras by means of unique singular strong unit. Recall that an MV -algebra A is hyperarchimedean [9,2] if for each x ∈ A there is an n ∈ N such that nx + nx = nx; and an l-group is hyperarchimedean [10] if all of its l-group homomorphic images are archimedean. Belluce [11,Theorem 4] shows that A is hyperarchimedean if and only if all prime ideals are maximal.…”

Section: A Problem Of Annihilator Primes In MV -Algebrasmentioning

confidence: 99%

A problem of annihilator primes in MV-algebras

Yang

2009

Journal of Pure and Applied Algebra

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Communicated by M. Broué MSC: 06D35 03G25 06D50 a b s t r a c t Using Mundici's equivalence [D. Mundici, Interpretation of AF C * -algebras in Łukasiewicz sentential calculus, J. Funct. Anal. 65 (1) (1986) 15-63] this note generalizes the result of [R. Cignoli, A. Torrens, The poset of prime l-ideals of an abelian l-group with strong unit, J. Algebra 184 (2) (1996) 604-612] for prime ideals and polars. Moreover, the generalization characterizes MV -algebras for which every prime ideal is the annihilator of a linear ordered ideal, and thus gives a negative answer to a problem of [L.P., Belluce, Semisimple algebras of infinite valued logic and bold fuzzy set theory, Canad. J. Math. 38 (6) (1986) 1356-1379]

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Section: A Problem Of Annihilator Primes In MV -Algebrasmentioning

confidence: 99%

A problem of annihilator primes in MV-algebras

Yang

2009

Journal of Pure and Applied Algebra

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“…Consider MV-algebras such that the minimal space Min(A) is compact with respect to the Zariski topology inherited by Spec(A). In [6] is proved that when Min(A) is compact, Min(A) is a Stone space. From this and Theorem 4.2 we have: It is easy to check that ≤ is an order relation with …”

Section: Mv-algebras With Min(a) Compactmentioning

confidence: 99%

“…any MV-algebra A, the space Min(A) with the topology inherited from the Zariski topology on Spec(A) is a Hausdorff zero-dimensional space, i.e., Min(A) is a Hausdorff space with a basis of clopen sets of the form r(a) = U (a) ∩ Min(A) = {P ∈ Min(A) : a /∈ P } (see[6], Section 5).…”

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confidence: 99%

Representations of MV-algebras by sheaves

Ferraioli¹,

Lettieri²

2011

Mathematical Logic Quarterly

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In this paper, inspired by methods of Bigard, Keimel, and Wolfenstein, we develop an approach to sheaf representations of MV-algebras which combines two techniques for the representation of MV-algebras devised by Filipoiu and Georgescu and by Dubuc and Poveda . Following Davey approach, we use a subdirect representation of MV-algebras that is based on local MV-algebras. This allowed us to obtain: (a) a representation of any MV-algebras as MV-algebra of all global sections of a sheaf of local MV-algebras on the spectruum of its prime ideals; (b) a representation of MV-algebras, having the space of minimal prime ideals compact, as MV-algebra of all global sections of a Hausdorff sheaf of MV-chains on the space of minimal prime ideals, which is a Stone space; (c) an adjunction between the category of all MV-algebras and the category of MV-algebraic spaces, where an MV-algebraic space is a pair (X; F), where X is a compact topological space and F is a sheaf of MValgebras with stalks that are local

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“…Recent developments, after the pioneering paper by Goguen,17 have emphasized deep and fruitful connection among MV algebras, fuzzy set theory, and fuzzy logic. 2,3,12,31 It is worth noting that MV algebras allow one to construct Hilbertian systems in fuzzy logic. 10,32 We adopt a simple axiomatization for MV algebras.…”

Section: MV Algebras and Linguistic Hedgesmentioning

confidence: 99%