On super-associative algebras with (2m,m)-quasigroup operations for m ≥ 2

ON m-STABLE COMMUTATIVE POWER- ASSOCIATIVE ALGEBRAS

A commutative power-associative algebra A of characteristic >5 with an idempotent u may be written1 as the supplementary sum ^=^4„(l)+4u(l/2)+^4u(0) where 4U(X) is the set of all xx in A with the property xx« =Xxx. The subspaces Au(l) and .4K(0) are orthogonal subalgebras, [AU(1/2)]2QAU(1)+AU(0) andAu(K)Au(l/2) C4„(l/2)+^4u(l—X) forX=0, 1. The algebra A is called w-stable if 4u(X)-4„(l/2)C.4u(l...

Weakly Associative Relation Algebras with Polyadic Composition Operations

We consider n ary relative products jn on subsets of a re exive and symmetric binary relation and de ne a variety of weakly associative relation algebras with polyadic composi tion operations WA A theorem that any A WA is representable over a re exive and symmetric relation is proved We also show that the equational theory of WA is decidable

Abstracts Local algebras of a differentiable quasigroup

On algebras with many symmetric operations

We show that, for each finite algebra A, either it has symmetric term operations of all arities or else some finite algebra in the variety generated by A has two automorphisms without a common fixed point. We also show this two-automorphism condition cannot be replaced by a single fixed-pointfree automorphism.

Integrable ODEs on Associative Algebras

In this paper we give definitions of basic concepts such as symmetries, first integrals, Hamilto-nian and recursion operators suitable for ordinary differential equations on associative algebras, and in particular for matrix differential equations. We choose existence of hierarchies of first integrals and/or symmetries as a criterion for integrability and justify it by examples. Using our compo...