Notes on P - Algebra ( 4 ) : Algebra over ProcessStructure , Part I .

We develop theory of algebra over processes, based on an abstract treatment of process structure. The abstract framework of process structures is developed (Part I), and, on its basis, theory of algebra is developed where the basic results including Birkho -like Variety Theorem are proved (Part II). We also discuss properties of signi cant concrete examples of algebras, taken from extant theories of concurrency. Part I develops the abstract theory of process structure encompassing a wide range of structures for process theory including concrete structures we have discussed in the preceding notes. The theory is used as foundations of the algebraic development in Part II, and is interesting in its own right.