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Algebraic ramifications of the common extension problem for group-valued measures

Rüdiger Göbel, R. Shortt (1994)

Fundamenta Mathematicae

Let G be an Abelian group and let μ: A → G and ν: B → G be finitely additive measures (charges) defined on fields A and B of subsets of a set X. It is assumed that μ and ν agree on A ∩ B, i.e. they are consistent. The existence of common extensions of μ and ν is investigated, and conditions on A and B facilitating such extensions are given.

Algorithm for the complement of orthogonal operations

Iryna V. Fryz (2018)

Commentationes Mathematicae Universitatis Carolinae

G. B. Belyavskaya and G. L. Mullen showed the existence of a complement for a k -tuple of orthogonal n -ary operations, where k < n , to an n -tuple of orthogonal n -ary operations. But they proposed no method for complementing. In this article, we give an algorithm for complementing a k -tuple of orthogonal n -ary operations to an n -tuple of orthogonal n -ary operations and an algorithm for complementing a k -tuple of orthogonal k -ary operations to an n -tuple of orthogonal n -ary operations. Also we find some...

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