多重分式约化III：区间幺半群的情形
Multifraction reduction III: The case of interval monoids
摘要：
我们调查gcd-幺半群，这是cancellative幺半群中的任何两个元素承认左和右gcd，和相关的减少的重分数（arXiv：1606.08991和1606.08995），一般的方法来的字问题的包络群。这里我们考虑与有限偏序集相关的区间幺半群的特殊情况。通过这种方式，我们构造了gcd-幺半群，其中重分数的约化具有尚未被认为是相容的规定性质：不收敛的约化的半收敛，达到一定水平但不超过的半收敛，不可嵌入到包络群中（半收敛的强否定）。
英文摘要：
We investigate gcd-monoids, which are cancellative monoids in which any two elements admit a left and a right gcd, and the associated reduction of multifractions (arXiv:1606.08991 and 1606.08995), a general approach to the word problem for the enveloping group. Here we consider the particular case of interval monoids associated with finite posets. In this way, we construct gcd-monoids, in which reduction of multifractions has prescribed properties not yet known to be compatible: semi-convergence of reduction without convergence, semi-convergence up to some level but not beyond, non-embeddability into the enveloping group (a strong negation of semi-convergence).
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。
