Morphisms, tensor products and σ-effect algebras

This paper first considers morphisms, bimorphisms, and tensor products of effect algebras. Various tensor products of specific types of effect algebras are computed. We then investigate σ-effect algebras, σ-morphisms, σ-bimorphisms, σ-tensor products and compute some specific σ-tensor products. Effective mappings on σ-effect algebras are introduced and studied. A class of mappings on a Hilbert space called quadratic state-forms is presented. A one-to-one correspondence between quadratic state-forms and σ-morphisms from a σ-effect algebra to a Hilbert space effect algebra is given.