幂等半域的等式理论
Equational theories of idempotent semifields
AI总结：
该研究解决幂等半域等式理论的公开问题，证明其非平凡理论无有限基、理论数量达连续统多个，且全体幂等半域类的等式理论为 co-NP 完全。
摘要：
本文回答了关于幂等半域等式理论的若干公开问题。具体而言，证明了：（i）任何非平凡幂等半域类的等式理论都不具有有限基；（ii）幂等半域类的等式理论有连续统多个；以及（iii）幂等半域类的等式理论是 co-NP 完全的。
英文摘要：
This paper provides answers to several open problems about equational theories of idempotent semifields. In particular, it is proved that (i) no equational theory of a non-trivial class of idempotent semifields has a finite basis; (ii) there are continuum-many equational theories of classes of idempotent semifields; and (iii) the equational theory of the class of idempotent semifields is co-NP-complete.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
