What is algebraic in process theory?

This is an extended version of an essay with the same title that I wrote for the workshop Algebraic Process Calculi: The First Twenty Five Years and Beyond, held in Bertinoro, Italy in the first week of August 2005. 1 Prologue In mathematics, sometimes two kinds of algebra are distinguished: elementary and Elementary algebra records the properties of the real number system, mostly in the form of equations using symbols to denote constants (particular real numbers) and variables (ranging over all real numbers). Elementary algebra is concrete in the sense that it is about one particular kind of object: the real number. algebra (also known as modern algebra) is concerned with the study of the (properties of the) fundamental operations of arithmetic in more generality, e.g., no longer talking about addition of real numbers only, but talking about addition of anything that might be worth adding. The generality is usually achieved by defining the fundamental operations axiomatically. For an...

• Type: Journal
• Year: 2006
• Where: ENTCS
• Authors: Bas Luttik
• Keywords: Algebra, Elementary Algebra, ENTCS 2006, Real Numbers