Generalizations of Samuel's criteria for a ring to be a unique factorization domain

Hurwitz级数环中的因式分解界与不可约性准则

Factorization Bounds and Irreducibility Criteria in Hurwitz Series Rings

该研究针对Hurwitz级数环，给出递归分解公式、因式分解长度界、Hurwitz-Newton多边形及不可约性准则，结合局部化方法整合多素元准则，并用整数环等实例验证结果。

Homological criteria for minimal multiplicity

Lower bounds on Hilbert-Samuel multiplicity are known for several types of commutative noetherian local rings, and rings with multiplicities which achieve these lower bounds are said to have minimal multiplicity. The first part of this paper gives characterizations of rings of minimal multiplicity in terms of the Ext-algebra of the ring; in particular, we show that minimal multiplicity can be detected via an Ext-algebra which is Gorenstein or Koszul AS-regular. The second part of this paper characterizes rings of minimal multiplicity via a numerical homological invariant introduced by J. Herzo…

唯一分解整环上多项式环的整除性

Some Divisibility Properties in Ring of Polynomials over a Unique Factorization Domain

利用多项式求值的方法，给出了多项式整除性的一些有用判据。这使我们能够开发有趣的结果有关的素元域的系数。特别地，可以证明在某些条件下，系数域必须有无穷多个素元。我们给出了D-环的替代特征，并给出了各种例子。

形式幂级数的一些因子分解结果

Some factorization results for formal power series

本文研究形式幂级数在主理想领域上的因子分解，给出精确的不可约因子数量界，并推导出形式幂级数的不可约性判别准则。

对数牛顿多边形与多胞体，以及狄利克雷多项式的因式分解

Logarithmic Newton polygons and polytopes, and the factorization of Dirichlet polynomials

本文通过引入对数牛顿多边形与对数牛顿多胞体等工具，绕过典范映射对整数素因子分解的依赖，建立了狄利克雷多项式的一系列不可约性、无平方因子性及绝对不可约性判据，推广了经典多项式因式分解理论。

Elementary matrix factorizations over Bézout domains

We study the homotopy category $\mathrm{hef}(R,W)$ (and its $\mathbb{Z}_2$-graded version $\mathrm{HEF}(R,W)$) of elementary factorizations, where $R$ is a Bézout domain which has prime elements and $W=W_0 W_c$, where $W_0\in R^\times$ is a square-free element of $R$ and $W_c\in R^\times$ is a finite product of primes with order at least two. In this situation, we give criteria for detecting isomorphisms in $\mathrm{hef}(R,W)$ and $\mathrm{HEF}(R,W)$ and formulas for the number of isomorphism classes of objects. We also study the full subcategory $\mathbf{hef}(R,W)$ of the homotopy category $\…