Algebraic structures of tropical mathematics

摘要

Tropical mathematics often is defined over an ordered cancellative monoid M, usually taken to be (R, +) or (Q,+). Although a rich theory has arisen from this viewpoint (cf. G.L. Litvinov, The Maslov dequantization, and idempotent and tropical mathematics; a brief introduction, 2005), idempotent semirings possess a restricted algebraic structure theory, and also do not reflect certain valuation-theoretic properties, thereby forcing researchers to rely often on combinatoric techniques.