Hyperidentities in algebras and varieties

Abstract

Three-dimensional numerical calculations of Heliac equilibria are presented. The results indicate that finite-/3 distortions in the flux surfaces can arise because of the presence of low order rational surfaces within or near the plasma. These distortions arise as a result of non-linear beatings between the toroidal shift and the helical components of the magnetic field. Reducing the toroidal shift by increasing the number of field periods and/or the aspect ratio improves the equilibrium |3-limit.

Binary Representations of Algebras With at Most Two Binary Operations: A Cayley Theorem for Distributive Lattices

“…The binary version of Cayley theorem was first proved for the multiplicative group of a field in [1] (also see [2]). The binary version of Cayley theorem for Boolean algebras is proved in [3] (also see [4][5][6]).…”

“…In this case the hyperidentity is called a hyperidentity of variety V . For example, if Q(·) is a distributive quasigroup, then the algebra Q(·, \, /) satisfies the hyperidentities of distributivity: [2]). If Q(A) is a medial quasigroup, then the algebra Q(A,…”

On t-stochastic algebras

“…These identities are formulas of the second order predicate calculus, for the first equation is a hyperidentity while the second and third equations are ∀∃ (∀) formulas [2]. The notion of stochastic algebra was introduced in [2] as the binary representation of the multiplicative semigroup (0, 1) of a linearly ordered field with the identities (1)- (3). Some results of topological stochastic algebras are considered in [3].…”

Subdirectly irreducible algebras with various equations

“…Theorem 1.2 (Movsisyan [3]). If the algebra A = (Q, ) with binary and unary operations satisfies the hyperidentities…”