关于某些非商超域上齐次线性方程的非平凡解
Nontrivial solutions for homogeneous linear equations over some non-quotient hyperfields
AI总结：
本文引入一类包含多种非商超域构造的超域，部分回答了Baker和Zhang关于超域上齐次线性方程组非零解的存在性问题，并纠正了文献中关于某类超域为非商超域的错误论断。
摘要：
我们引入了一类超域，其中包含若干非商超域的构造。随后，我们利用它部分回答了M. Baker和T. Zhang提出的一个问题：未知数个数多于方程个数的齐次线性方程组是否总有非零解？我们还考虑了文献中声称是非商超域的一类超域，并证明这一说法是错误的。
英文摘要：
We introduce a class of hyperfields which includes several constructions of non-quotient hyperfields. We then use it to partially answer a question posed by M. Baker and T. Zhang: Does a system of homogeneous linear equations with more unknowns than equations always have a nonzero solution? We also consider a class of hyperfields that was claimed in the literature to be non-quotient, and show that this is false.
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。
