双幂等半环上矩阵的置换性
Permutability of Matrices over Bipotent Semirings
摘要：
本文研究了交换双幂半环（其中最著名的例子是热带半环）上矩阵半群的置换性质。我们证明了每一个这样的半群是弱置换（结果以前在文献中指出，但与错误的证明），然后继续深入研究的问题时，他们是强置换（这在很大程度上取决于半环）。在此过程中，我们对单演双幂半环进行了分类，并描述了截断热带半环之间的所有同构。
英文摘要：
We study permutability properties of matrix semigroups over commutative bipotent semirings (of which the best-known example is the tropical semiring). We prove that every such semigroup is weakly permutable (a result previous stated in the literature, but with an erroneous proof) and then proceed to study in depth the question of when they are strongly permutable (which turns out to depend heavily on the semiring). Along the way we classify monogenic bipotent semirings and describe all isomorphisms between truncated tropical semirings.
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。
