Some characterizations of partial algebras

Partial algebras arise frequently in applications, especially in quantum theory where observables are represented by unbounded linear maps that are often not conformable for multiplication. In this paper, we introduce a certain class of partial algebras and prove, among other results, that every partial algebra belonging to the class may be identified with a partial subalgebra of some algebra. This furnishes a means of studying the members of the class by exploiting known results about algebras.