QUASI-BOOLEAN POWER OF ALGEBRAS AND IDEMPOTENT ALGEBRAS

In this paper we provide a necessity condition for embedding of the binary algebra into the quasi-boolean power of a rectangular algebra. It is also proved that every idempotent and hyperassociative algebra via the weak bihomomorphism maps in an idempotent and commutative algebra.

MV-Partitions and MV-Powers

In this chapter, the authors generalize the Boolean partition to semisimple MV-algebras. MV-partitions together with a notion of refinement is tantamount a construction of an MV-power, analogous to Boolean power construction (Mansfield, 1971). Using this new notion we introduce the corresponding theory of MV-powers.

Towards a calculus of algorithms

We develop a generalised polynomial formalism which captures the concept of an algebra of piece-wise denned polynomials. The formalism is based on the Boolean power construction of universal algebra. A generalisation of the theory of substitution homomorphisms is developed. The abstract operation of composition of generalised polynomials in one variable is denned and shown to correspond to function composition.

QE rings in characteristic pn

We show that all QE rings of prime power characteristic are constructed in a straightforward way out of three components: a filtered Boolean power of a finite field, a nilpotent Jacobson radical, and the ring Zp. or the Witt ring W2(F4) (which is the characteristic four analogue of the Galois field with four elements).