A note on the lattice definability of Bernstein algebras.
Algèbres non-associatives et applications à la génétique
Commutator algebras arising from splicing operations
We prove that the variety of Lie algebras arising from splicing operation coincides with the variety CM of centreby-metabelian Lie algebras. Using these Lie algebras we find the minimal dimension algebras generated the variety CM and the variety of its associative envelope algebras. We study the splicing n-ary operation. We show that all n-ary (n > 2) commutator algebras arising from this operation are nilpotent of index 3. We investigate the generalization of the splicing n-ary operation, and...
Genetic Algebras Studied Recursively and by Means of Differential Operators.
Genetické algebry. Věnováno prof. RNDr. Ladislavu Procházkovi, DrSc., k jeho 75. narozeninám
Modular Bernstein algebras.
One-dimensional subalgebras of a Bernstein algebra.
Sur les algèbres de Jordan génétiques
The structure and representation of n-ary algebras of DNA recombination
In this paper we investigate the structure and representation of n-ary algebras arising from DNA recombination, where n is a number of DNA segments participating in recombination. Our methods involve a generalization of the Jordan formalization of observables in quantum mechanics in n-ary splicing algebras. It is proved that every identity satisfied by n-ary DNA recombination, with no restriction on the degree, is a consequence of n-ary commutativity and a single n-ary identity of the degree 3n-2....
Признак генетичности конечно-порожденных бернштейновских алгебр.