半环诱导赋值代数同构与半环同构之间的关系
On the Relationship Between Semiring-Induced Valuation Algebra Isomorphisms and Semiring Isomorphisms
首次发表
浏览论文内容
中文总结 AI 辅助
本文探究半环同构与诱导赋值代数同构的双向关系，证明半环同构可推出赋值代数同构，且对特定半环，赋值代数同构也能推出底层半环同构。
中文摘要 AI 辅助
本文建立了半环同构与其诱导赋值代数同构之间的双向关系。研究表明，半环同构足以推出赋值代数同构；反之，对于无乘法幂等零因子的加法幂等半环，赋值代数同构的存在性意味着其底层半环是同构的。
英文摘要
This paper establishes a bidirectional relationship between isomorphisms of semirings and isomorphisms of their induced valuation algebras. We show that a semiring isomorphism is sufficient for a valuation algebra isomorphism. Conversely, for additively idempotent semirings without multiplicatively idempotent zero divisors, the existence of a valuation algebra isomorphism implies that the underlying semirings are isomorphic.
