we investigate the problem of the existence of a frame forright ideals of a c*-algebra a, without the use of the kasparov stabilizationtheorem. we show that this property can not characterize a as a c*-algebraof compact operators.

We re-examine the appearance of semiheaps and (para-associative) ternary algebras in quantum mechanics. In particular, we review construction a semiheap on Hilbert space set bounded operators space. The new aspect this work is discussion how symmetries system induce homomorphisms relevant algebras.

We determine precisely those locally finite varieties of unary algebras of finite type which, when augmented by a ternary discriminator, generate a variety with a decidable theory.

Lie algebras endowed with an action by automorphisms of any of the symmetric groups S3 or S4 are considered, and their decomposition into a direct sum of irreducible modules for the given action is studied. In case of S3-symmetry, the Lie algebras are coordinatized by some nonassociative systems, which are termed generalized Malcev algebras, as they extend the classical Malcev algebras. These s...