Distributive groupoids and preradicals. I.
We present an elementary proof (purely in equational logic) that distributive groupoids are symmetric-by-medial.
We introduce a concept of implication groupoid which is an essential generalization of the implication reduct of intuitionistic logic, i.e. a Hilbert algebra. We prove several connections among ideals, deductive systems and congruence kernels which even coincide whenever our implication groupoid is distributive.
This note contains Sylow's theorem, Lagrange's theorem and Hall's theorem for finite Bruck loops. Moreover, we explore the subloop structure of finite Bruck loops.
We have designed three fast implementations of a recently proposed family of hash functions Edon–. They produce message digests of length bits and project security of hash computations for finding collisions and hash computations for finding preimages and second preimages. The design is not the classical Merkle-Damgård but can be seen as wide-pipe iterated compression function. Moreover the design is based on using huge quasigroups of orders , and that are constructed by using only bitwise...
Let be a partial latin square and be a latin square with . We say that is a latin trade if there exists a partial latin square with such that is a latin square. A -homogeneous latin trade is one which intersects each row, each column and each entry either or times. In this paper, we show the existence of -homogeneous latin trades in abelian -groups.
We modify tools introduced in [Daly D., Vojtěchovský P., Enumeration of nilpotent loops via cohomology, J. Algebra 322 (2009), no. 11, 4080–4098] to count, for any odd prime , the number of nilpotent loops of order up to isotopy, instead of isomorphy.
We first discuss the construction by Pérez-Izquierdo and Shestakov of universal nonassociative enveloping algebras of Malcev algebras. We then describe recent results on explicit structure constants for the universal enveloping algebras (both nonassociative and alternative) of the 4-dimensional solvable Malcev algebra and the 5-dimensional nilpotent Malcev algebra. We include a proof (due to Shestakov) that the universal alternative enveloping algebra of the real 7-dimensional simple Malcev algebra...