与Shuffle乘积相容的同余式
Congruences Compatible with the Shuffle Product
摘要：
本文主要研究半环中可被赋予系数混洗积的幺半群。我们证明了，当重数不属于一个具有素特征的环时，这样的么半群是迹么半群。当特征是素数时，我们给出了同余$\equiv$（或关系元$R$）的一个分解，使得$A^*/\_\equiv=< A; R>$允许一个混洗积。这种分解只涉及把本原元加到相继的本原元上。最后，我们研究了与Magnus变换的相容性，并考察了同余对于某些权函数是齐次的情况。对于深度1的同余，也证明了这样一个权函数的存在性.
英文摘要：
This article is devoted to the study of monoids which can be endowed with a shuffle product with coefficients in a semiring. We show that, when the multiplicities do not belong to a ring with prime characteristic, such a monoid is a monoid of traces. When the characteristic is prime, we give a decomposition of the congruences $\equiv$ (or relators $R$) such that $A^*/\_\equiv=< A; R>$ admits a shuffle product. This decomposition involves only addition of primitive elements to the successive quotients. To end with, we study the compatibility with Magnus transformation and examine the case of congruences which are homogeneous for some weight function. The existence of such a weight function is also showed for congruences of depth one.
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。
