Generalized morphisms of abelian m-ary groups
We prove that the set of all n-ary endomorphisms of an abelian m-ary group forms an (m,n)-ring.
We prove that the set of all n-ary endomorphisms of an abelian m-ary group forms an (m,n)-ring.
A method of generating a practically unlimited number of quasigroups of a (theoretically) arbitrary order using the computer algebra system Maple 7 is presented. This problem is crucial to cryptography and its solution permits to implement practical quasigroup-based endomorphic cryptosystems. The order of a quasigroup usually equals the number of characters of the alphabet used for recording both the plaintext and the ciphertext. From the practical viewpoint, the most important quasigroups are of...
On the unit sphere in a real Hilbert space , we derive a binary operation such that is a power-associative Kikkawa left loop with two-sided identity , i.e., it has the left inverse, automorphic inverse, and properties. The operation is compatible with the symmetric space structure of . is not a loop, and the right translations which fail to be injective are easily characterized. satisfies the left power alternative and left Bol identities “almost everywhere” but not everywhere....
We show that group conjugation generates a proper subvariety of left distributive idempotent groupoids. This subvariety coincides with the variety generated by all cancellative left distributive groupoids.