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arXiv · 2608.09961

On the Relationship Between Semiring-Induced Valuation Algebra Isomorphisms and Semiring Isomorphisms

Xuechong Guan
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Abstract

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.

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Xuechong Guan. 2026-07-25. On the Relationship Between Semiring-Induced Valuation Algebra Isomorphisms and Semiring Isomorphisms. https://arxiv.org/abs/2608.09961

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