环沿理想的合并复制中的Prüfer型条件

环沿乘-典范理想的合并复制

The amalgamated duplication of a ring along a multiplicative-canonical ideal

在简要地回顾了环$R$沿理想$I$的合并复制的主要性质之后，我们将注意力限制在当$I$是$R$ \cite{hhp}的乘法典型理想时，$R\JoinI$的性质的研究上。特别地，我们研究了$R\Join I$的每一个正则分式理想何时是可除的.

环沿理想的合并复制上的素子模与弱素子模

Prime and weakly prime submodules on amalgamated duplication of a ring along an ideal

本文研究了有单位元交换环 $A$ 的模 $M$ 沿理想 $I$ 的合并复制 $M \bowtie I$ 上的素子模与弱素子模形式，并给出了相关结果与示例。

环沿理想的融合复制的扩展零因子图

The extended zero-divisor graph of the amalgamated duplication of a ring along an ideal

本文研究环沿理想的融合复制的扩展零因子图，刻画其与零因子图重合及完全性的条件，并计算直径和围长。

沿理想的融合代数中素理想链的性质

Properties of chains of prime ideals in an amalgamated algebra along an ideal

设$f:A \to B$是环同态，$J$是$B$的理想.在本文中，我们研究了$A$与$B$沿着$J$的合并，关于$f$（记为${A\Join^fJ}$），一个构造，它为研究环沿着理想的合并复制提供了一个通用框架，由D'Anna和Fontana在2007年引入和研究，以及其他经典构造（如$A+ XB[X]$，$A+ XB[[X]]$和$D+M$构造）。特别是，我们完整地描述了合并重复的素谱，我们给出了其Krull维数的界。

Tangent cones of monomial curves obtained by numerical duplication

Given a numerical semigroup ring $R=k[\![S]\!]$, an ideal $E$ of $S$ and an odd element $b \in S$, the numerical duplication $S \! \Join^b \! E$ is a numerical semigroup, whose associated ring $k[\![S \! \Join^b \! E]\!]$ shares many properties with the Nagata's idealization and the amalgamated duplication of $R$ along the monomial ideal $I=(t^e \mid e\in E)$. In this paper we study the associated graded ring of the numerical duplication characterizing when it is Cohen-Macaulay, Gorenstein or complete intersection. We also study when it is a homogeneous numerical semigroup, a property that is …

关于强$(a)$ -环

On Strong $(a)$-Rings

本文引入了强性质$(A)$，并研究了性质$(A)$和强性质$(A)$在平凡环扩张和环沿理想的合并复制中的转移.我们还证明了一类满足性质$(A)$而不满足强性质$(A)$的环.

沿理想的双并合代数

Bi-Amalgamated algebras along ideals

设$f: A\rightarrow B$和$g: A\rightarrow C$是两个交换环同态，$J$和$J'$分别是$B$和$C$的两个理想，使得$f^{-1}(J)=g^{-1}(J')$ . $A$的$(B, C)$沿着$(J, J')$关于$(f,g)$的\emph{bi-amalgamation}是由$$A\bowtie^{f,g}(J,J'):=\big\{(f(a)+j,g(a)+j') \mid a\in A, (j,j')\in J\times J'\big\}.$$给出的$B\times C$的子环。本文研究了\emph{bi-amalgamations}的环论性质，并利用以前的工作进行了各种设置的拉回和合并。在第二节和第三节中，我们提供了双合并的例子，并展示了这些结构是如何作为回撤出现的。第四部分研究了一些基本环理论性质到双合并的转移，第五部分致力于这些结构的素理想结构。所有新的结果同意最近的研究文献中的D 'Anna-Finocchiaro-Fontana的合并和重复。

Algebraic and topological properties of an amalgamated algebra along an ideal

Let $f:A \rightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we study the amalgamation of $A$ with $B$ along $J$ with respect to $f$, a construction that provides a general frame for studying the amalgamated duplication of a ring along an ideal, introduced by D'Anna and Fontana in 2007, and other classical constructions (such as the $A+ XB[X]$, the $A+ XB[\![X]\!]$ and the $D+M$ constructions). In particular, we completely describe the prime spectrum of the amalgamation and, when it is a local Noetherian ring, we study its embedding dimension and when it turns …

沿理想的合并代数

Amalgamated algebras along an ideal

设$f:A \to B$是环同态，$J$是$B$的理想.在本文中，我们开始了一个新的环结构称为“融合的$A$与$B$沿$J$关于$f$“的系统研究。这种结构可以在J.L. Dorroh出现于1932年，提供了一个研究环沿着理想的合并复制的一般框架，由D'Anna和Fontana在2007年引入和研究，以及其他经典结构，如$A+ XB[X]$和$A+ XB[[X]]$结构，Boisen和Sheldon的CPI扩展，$D+M$结构和Nagata的理想化。

Commutative rings with invertible-radical factorization

In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties under homomorphic image and their transfer to various contexts of constructions such as direct product, trivial ring extension and amalgamated duplication of a ring along an ideal. Our results generate examples that enrich the current literature with new and original families of rings satisfying these properties.

由Bézout-like条件定义的环的归并

Amalgamation of rings defined by bézout-like conditions

设$f:A\lo B$是环同态，$J$是$B.$的理想本文研究了初等因子环、Hermite环和Bézout环等概念到合并环$A\bowtie^fJ.$的迁移，给出了$ A\bowtie^fJ$是初等因子环的充要条件，其中$A$和$B$是整环.证明了$ A\bowtie^fJ$是Hermite环当且仅当它是Bézout环.特别是，我们研究了前面的概念转移到一个环$A$沿着$Q(A)$的$A-$子模块$E$的合并复制，使得$E^2\subseteq E.$

Ulrich ideals and 2-AGL rings

The notion of 2-almost Gorenstein local ring (2-AGL ring for short) is a generalization of the notion of almost Gorenstein local ring from the point of view of Sally modules of canonical ideals. In this paper, for further developments of the theory, we discuss three different topics on 2-AGL rings. The first one is to clarify the structure of minimal presentations of canonical ideals, and the second one is the study of the question of when certain fiber products, so called amalgamated duplications are 2-AGL rings. We also explore Ulrich ideals in 2-AGL rings, mainly two-generated ones.

Families of Gorenstein and almost Gorenstein rings

Starting with a commutative ring $R$ and an ideal $I$, it is possible to define a family of rings $R(I)_{a,b}$, with $a,b \in R$, as quotients of the Rees algebra $\oplus_{n \geq 0} I^nt^n$; among the rings appearing in this family we find Nagata's idealization and amalgamated duplication. Many properties of these rings depend only on $R$ and $I$ and not on $a,b$; in this paper we show that the Gorenstein and the almost Gorenstein properties are independent of $a,b$. More precisely, we characterize when the rings in the family are Gorenstein, complete intersection, or almost Gorenstein and we …