In this paper, as homage to Professor Gaspar Mayor in his 70 anniversary, we present a summary of results on BL-algebras and related structures that, using the one-to-one correspondence between divisible finite t-norms and finite BL-chains, allows us to provide an equational characterization of any divisible finite t-norm.

Let (G, ·) be a 2-divisible group and let (G∗,+) be a uniquely divisible abelian group. We show that the alternative quadratic functional equation f (x y−1)+ f (x y) =±2( f (x)+ f (y)) is equivalent to the quadratic functional equation f (x y−1)+ f (x y) = 2 f (x)+2 f (y) for the class of functions f : G→ G∗.

Let X be a p-divisible group over a regular scheme S such that the Newton polygon in each geometric point of S is the same. Then there is a p-divisible group isogenous to X which has a slope filtration.

We study the global structure of moduli spaces of quasiisogenies of polarized p-divisible groups introduced by Rapoport and Zink. Using the corresponding results for non-polarized p-divisible groups from a previous paper, we determine their dimensions and their sets of connected components and of irreducible components. 2000 Mathematics Subject Classification: 14L05, 14K10 (Primary) 14G35 (Seco...

Divisible E-cash has been introduced twenty years ago but no construction is both fully secure in the standard model and efficiently scalable. In this paper, we fill this gap by providing an anonymous divisible E-cash construction with constant-time withdrawal and spending protocols. Moreover, the deposit protocol is constant-time for the merchant, whatever the spent value is. It just has to co...

The aim of this paper is to present a construction of t-divisible designs for t > 3, because such divisible designs seem to be missing in the literature. To this end, tools such as finite projective spaces and their algebraic varieties are employed. More precisely, in a first step an abstract construction, called t-lifting, is developed. It starts from a set X containing a tdivisible design and...