1,560 research outputs found

    Probability Metric Space on MV-Algebras

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    AbstractBy means of the probability measure theory of MV-algebras we introduce the concepts of probability truth degrees of the elements of MV-algebra and probability similarity degrees between elements, and then define therefrom three probability metric spaces on MV-algebra, and get some good results

    Convergences in perfect BL-algebras

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    The aim of the paper is to investigate some concepts of convergence in the class of perfect BL-algebras. Similarity convergence was developed by G. Georgescu and A. Popescu in the case of the residuated lattices, while the convergence with a fixed regulator was studied by CernĂĄk for lattice-ordered groups and MV-algebras and by the author for residuated lattices. In this paper we study the similarity convergence and the convergence with a fixed regulator for the perfect BL-algebras. The main result is the construction of Cauchy completion of a perfect BL-algebra.Peer Reviewe

    Canonical matrices for linear matrix problems

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    We consider a large class of matrix problems, which includes the problem of classifying arbitrary systems of linear mappings. For every matrix problem from this class, we construct Belitskii's algorithm for reducing a matrix to a canonical form, which is the generalization of the Jordan normal form, and study the set C(m,n) of indecomposable canonical m-by-n matrices. Considering C(m,n) as a subset in the affine space of m-by-n matrices, we prove that either C(m,n) consists of a finite number of points and straight lines for every (m,n), or C(m,n) contains a 2-dimensional plane for a certain (m,n).Comment: 59 page

    Interval valued (\in,\ivq)-fuzzy filters of pseudo BLBL-algebras

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    We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued (\in,\ivq)-fuzzy filters of pseudo BLBL-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval valued fuzzy filters are derived. The relationship among these generalized interval valued fuzzy filters of pseudo BLBL-algebras is considered. Finally, we consider the concept of implication-based interval valued fuzzy implicative filters of pseudo BLBL-algebras, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed

    On fixed points of self maps of the free ball

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    In this paper, we study the structure of the fixed point sets of noncommutative self maps of the free ball. We show that for such a map that fixes the origin the fixed point set on every level is the intersection of the ball with a linear subspace. We provide an application for the completely isometric isomorphism problem of multiplier algebras of noncommutative complete Pick spaces

    On the residue fields of Henselian valued stable fields, II

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    Let EE be a primarily quasilocal field, M/EM/E a finite Galois extension and DD a central division EE-algebra of index divisible by [M ⁣:E][M\colon E]. In addition to the main result of Part I, this part of the paper shows that if the Galois group G(M/E)G(M/E) is not nilpotent, then MM does not necessarily embed in DD as an EE-subalgebra. When EE is quasilocal, we find the structure of the character group of its absolute Galois group; this enables us to prove that if EE is strictly quasilocal and almost perfect, then the divisible part of the multiplicative group E∗E ^{\ast} equals the intersection of the norm groups of finite Galois extensions of EE.Comment: 10 page
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