Krasner algebras (Q2707102)

Building on early ideas and results of M. Krasner and others on cylindric algebras and Galois theory, the author of this comprehensive and readable book summarizes in an elegant manner most of what is known about algebras of Krasner type. The broad range of interesting topics include: relations and operations on relations; invariant and strongly invariant relations; Galois relation sets; locally invertible monoids; distributive and Boolean systems; diagonal elements; representation for denumerable Krasner algebras; Krasner algebras and congruence lattices; and formulas of the predicate calculus. Further, there is an extensive world-wide bibliography of works (56 items) related to Krasner algebras, which is most valuable. Finally, the author poses several difficult unsolved (1999) problems concerning Krasner algebras and related formal structures. E.g., concerning development of a useful duality theory for Krasner algebras. This reviewer believes the ideas of Krasner algebras are applicable to the design of high-speed distributed computing systems.