Power Algebras over Semirings

Focusing on the translation of structured sets RA, where R is a semiring and A is a structured set, this monograph explores the interplay between diverse mathematical topics and theoretical computer science. It introduces concepts like "idempotent analysis" and optimization theory while addressing foundational issues in mathematics. The work is exploratory, emphasizing the philosophical question of the dependence of algebra and topology on set theory, highlighting the complexity of definitions proposed by various researchers in this evolving field.