非交换整环的不可约因子图类型，II
Types of Irreducible Divisor Graphs of Noncommutative Domains, II
AI总结：
本文推广非交换整环中的不可约因子图，提出不可约因子单纯复形与 τ-不可约因子图，并据此刻画 n-唯一分解整环。
摘要：
本文继续研究文献[7]中引入的、分别针对 x∈D*\U(D) 的有向与无向不可约因子图概念 G(x) 和 Γ(x)。在此基础上，我们引入这些概念的两种推广。第一种是非交换原子整环 D 中针对 x∈D*\U(D) 的不可约因子单纯复形 S(x)，它同时推广了 R. Baeth 和 J. Hobson 在文献[3]中引入的交换情形。第二种是在非交换 τ-原子整环 D 中，针对 x∈D*\U(D) 的有向与无向 τ-不可约因子图 Gτ(x) 和 Γτ(x)，其中 D*\U(D) 上的关系 τ 是对称的且保持相伴关系。这些图同样推广了 C. P. Mooney 在文献[5]中引入的交换情形。此外，我们推广文献[3]和[5]的结果，通过这两种推广给出 n-唯一分解整环的刻画。
英文摘要：
In this paper, we continue investigation of the directed and undirected irreducible divisor graph concepts $G(x)$ and $Γ(x)$ of $x\in D^{\ast} \backslash U(D)$, respectively, which were introduced in [7]. Consequently, we introduce two generalizations of these concepts. The first one is the irreducible divisor simplicial complex $S(x)$ of $x\in D^{\ast} \backslash U(D)$ in a noncommutative atomic domain $D$, which simultaneously extends the commutative case that was introduced by R. Baeth and J. Hobson in [3]. The second one is the directed and undirected $τ$-irreducible divisor graphs $G_{τ}(x)$ and $Γ_{τ}(x)$ of $x\in D^{\ast} \backslash U(D)$, respectively, in a noncommutative $τ$-atomic domain $D$ with a symmetric and associate preserving relation $τ$ on $D^{\ast} \backslash U(D)$. Those graphs also extend the commutative case that was introduced by C. P. Mooney in [5]. Furthermore, we extend the results of [3] and [5] to give a characterization of n-unique factorization domains via those two generalizations.
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。
