论文标题
伪 - 硫酸盐邻域和偏斜的laurent多项式在FIR上
Pseudo-Sylvester domains and skew Laurent polynomials over firs
论文作者
论文摘要
在Jaikin-Zapirain的最新工作的基础上，我们为戒指提供了同源标准，使其成为伪Sylvester域，也就是说，可以承认一个分数圈环，所有分数圈都可以稳定地完全矩阵可逆。我们使用标准在自由理想环（FIRS）上研究偏斜的Laurent多项式环。作为我们方法的应用，我们证明，与自由{无限循环}的划分环的产品越过了分裂环，而表面组则是伪 - 硅化剂域无条件地和sylvester域，并且仅当他们承认稳定的自由取消率时。这取决于Farrell的最新证明 - 琼斯的猜想是通常的无多聚群，并扩展了Linnell-lück和Jaikin-Zapirain对这种跨产品的通用局部定位和通用领域的先前结果。
Building on recent work of Jaikin-Zapirain, we provide a homological criterion for a ring to be a pseudo-Sylvester domain, that is, to admit a division ring of fractions over which all stably full matrices become invertible. We use the criterion to study skew Laurent polynomial rings over free ideal rings (firs). As an application of our methods, we prove that crossed products of division rings with free-by-{infinite cyclic} and surface groups are pseudo-Sylvester domains unconditionally and Sylvester domains if and only if they admit stably free cancellation. This relies on the recent proof of the Farrell--Jones conjecture for normally poly-free groups and extends previous results of Linnell--Lück and Jaikin-Zapirain on universal localizations and universal fields of fractions of such crossed products.
