Power Algebras over Semirings

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Focusing on the exploration of semirings and their applications, this monograph delves into the structures of sets formed by RA, where R is a semiring. It seeks to establish a natural translation of these structures, bridging various mathematical and theoretical computer science topics, including formal language theory and fuzzy algebraic structures. Unlike previous works, this text adopts a more exploratory approach, grappling with foundational philosophical questions about the relationship between algebra, topology, and set theory amidst ongoing research in the field.