45 research outputs found

    Some Pre-filters in EQ-Algebras

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    In this paper, the notion of an obstinate prefilter (filter) in an EQ-algebra ξ is introduced and a characterization of it is obtained by some theorems. Then the notion of maximal prefilter is defined and is characterized under some conditions. Finally, the relations among obstinate, prime, maximal, implicative and positive implicative prefilters are studied

    On the Category of EQ-algebras

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    In this paper, we studied the category of EQ-algebras and showed that it is complete, but it is not cocomplete, in general. We proved that multiplicatively relative EQ-algebras have coequlizers and we calculated coproduct and pushout in a special case. Also, we constructed a free EQ-algebra on a singleton

    Characterizations of Some Fuzzy Prefilters (Filters) in E

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    We introduce and study some types of fuzzy prefilters (filters) in EQ-algebras. First, we present several characterizations of fuzzy positive implicative prefilters (filters), fuzzy implicative prefilters (filters), and fuzzy fantastic prefilters (filters). Next, using their characterizations, we mainly consider the relationships among these special fuzzy filters. Particularly, we find some conditions under which a fuzzy implicative prefilter (filter) is equivalent to a fuzzy positive implicative prefilter (filter). As applications, we obtain some new results about classical filters in EQ-algebras and some related results about fuzzy filters in residuated lattices

    nn-Fold Filters of EQ-Algebras

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    In this paper, we apply the notion of nn-fold filters to the EQEQ-algebras and introduce the concepts of nn-fold pseudo implicative, nn-fold implicative, nn-fold obstinate, nn-fold fantastic prefilters and filters on an EQEQ-algebra E\mathcal{E}. Then we investigate some properties and relations among them. We prove that the quotient algebra E/F\mathcal{E}/F modulo an 1-fold pseudo implicative filter of an EQEQ-algebra E\mathcal{E} is a good EQEQ-algebra and the quotient algebra E/F\mathcal{E}/F modulo an 1-fold fantastic filter of a good EQEQ-algebra E\mathcal{E} is an IEQIEQ-algebra

    Quantisation of derived Poisson structures

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    We prove that every 00-shifted Poisson structure on a derived Artin nn-stack admits a curved AA_{\infty} quantisation whenever the stack has perfect cotangent complex; in particular, this applies to LCI schemes. Where the Kontsevich-Tamarkin approach to quantisation hinges on invariance of the Hochschild complex under affine transformations, we instead exploit the observation that it carries an anti-involution, and that such anti-involutive deformations of the complex of polyvectors are essentially unique.Comment: 27 pp; v2 argument simplified and Artin section removed; v3 added long section extending to Artin n-stacks via differential operator

    Quantisation of derived Poisson structures

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