69 research outputs found
Further generalizations of the parallelogram law
In a recent work of Alessandro Fonda, a generalization of the parallelogram law in any dimension was given by considering the ratio of the quadratic mean of the measures of the -dimensional diagonals to the quadratic mean of the measures of the faces of a parallelotope. In this paper, we provide a further generalization considering not only -dimensional diagonals and faces, but the -dimensional ones for every
Tying up baric algebras
Given two baric algebras and we describe a
way to define a new baric algebra structure over the vector space , which we shall denote . We
present some easy properties of this construction and we show that in the
commutative and unital case it preserves indecomposability. Algebras of the
form in the associative, coutable-dimensional,
zero-characteristic case are classified.Comment: To appear in Mathematica Slovac
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