1,560 research outputs found
Probability Metric Space on MV-Algebras
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
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
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 -algebras
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 -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 -algebras
is considered. Finally, we consider the concept of implication-based interval
valued fuzzy implicative filters of pseudo -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
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
Let be a primarily quasilocal field, a finite Galois extension and
a central division -algebra of index divisible by . In
addition to the main result of Part I, this part of the paper shows that if the
Galois group is not nilpotent, then does not necessarily embed in
as an -subalgebra. When is quasilocal, we find the structure of the
character group of its absolute Galois group; this enables us to prove that if
is strictly quasilocal and almost perfect, then the divisible part of the
multiplicative group equals the intersection of the norm groups of
finite Galois extensions of .Comment: 10 page
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