Local gauss sums.
In this note it is shown that the closure condition, XY = XY, XY = XY, XY = XY --> XY = XY, (and its dual) is equivalent to the Thomsen condition in quasigroups but not in general. Conditions are also given under which groupoids satisfying it are principal homotopes of cancellative, abelian semigroups, or abelian groups.
Building upon earlier work in which axioms were formulated for multivariate measures of concordance, we examine properties of such measures. In particular,we examine the relations between the measure of concordance of an n-copula and the measures of concordance of the copula’s marginals.
We extend the definition of Markov operator in the sense of J. R. Brown and of earlier work of the authors to a setting appropriate to the study of n-copulas. Basic properties of this extension are studied.
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