Abolfazl Tarizadeh
Let $R$ be a commutative ring with the unit element. It is shown that an ideal $I$ in $R$ is pure if and only if Ann$(f)+I=R$ for all $f\in I$. If $J$ is the trace of a projective $R$-module $M$, we prove that $J$ is generated by the ``coordinates" of $M$ and $JM = M$. These lead to a few new results and alternative proofs for some known results.
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。
继续探索
Trace ideals, conductors, and ideals of finite (phantom) projective dimension
本文研究了特定理想是否包含于商环具有限幻影投射维数的理想中，证明了在准Gorenstein完全局部整环中不存在此类包含，并构造Cohen-Macaulay局部环的例子否定了Huneke-Swanson的问题。
We give a result of Auslander-Ringel-Tachikawa type for Gorenstein-projective modules over a complete Gorenstein order. In particular, we prove that a complete Gorenstein order is of finite Cohen-Macaulay representation type if and only if every indecomposable pure-injective object in the stable category of Gorenstein-projective modules is compact.
Let $R$ be a ring. An $R$-module $M$ is said to be an absolutely $w$-pure module if and only if $\Ext^1_R(F,M)$ is a GV-torsion module for any finitely presented module $F$. In this paper, we introduce and study the concept of $w$-FP-projective module which is in some way a generalization of the notion of $\rm FP$-projective module. An $R$-module $M$ is said to be $w$-$\rm FP$-projective if $\Ext^1_R(M,N)=0$ for any absolutely $w$-pure module $N$. This new class of modules will be used to characterize (Noetherian) $DW$ rings. Hence, we introduce the $w$-$\rm FP$-projective dimensions of module…
A generalization of strongly Gorenstein projective modules
本文推广了作者在J. Pure Appl. Algebra 210（2007）437- 445中的思想。也就是说，我们定义并研究了Gorenstein投射模的一种特殊情况。我们研究了这类新模的环的一些变化结果。给出了不一定是诺特环上的例子。
On containment of trace ideals in ideals of finite homological dimension
本文研究了迹理想包含于有限投射或内射维数理想的障碍，证明了Gorenstein完备局部域上big Cohen--Macaulay模的迹理想不能包含于任何有限投射维数理想中，推广了Smith的结果，并给出了相关迹理想的m-adic阶上界及自由分解映射元素理想的类似结论。
Varieties with ample Frobenius-trace kernel
研究正则变种上福布斯迹核的正性，发现其在射影空间中为 ample，但仅在 Picard 等级为 1 的 Fano 变种上成立。
A Linear Bound on the Projective Dimension of Height 3 Quadratic Ideals
本文给出高度为3的二次理想射影维数的线性上界，改进了Stillman问题的界。
Gorenstein homology, relative pure homology and virtually Gorenstein rings
我们考虑以下问题：Gorenstein同调是X-纯同调，在这个意义上定义的沃菲尔德，一类X的模块？设GP表示Gorenstein投射模类.证明了有限克鲁尔维数的交换诺特环R上的Gorenstein同调是GP-纯同调的充要条件是R实质上是Gorenstein.
Poincare series of some pure and mixed trace algebras of two generic matrices
我们研究特征为零的域K。对n小于或等于6，给出了两个一般n × n矩阵x和y的GL_n-不变量代数C_{n,2}和GL_n-伴随代数T_{n,2}的Poincare级数.简单分级和双分级的情况都包括在内。n最多为4的情况以前是已知的。当n=5或6时，我们证明了C_{n,2}没有参数的二阶系统.对于代数C_{4,2}和C_{5,2}，我们构造了生成元的极小集，并给出了Specht关于两个复矩阵酉相似定理的一个应用.本文对上述各种庞加莱级数的分子和子提出了五点建议。给出了一些启发式公式和待解决的问题。
Let $R$ be a commutative ring. We show that pure injective resolutions and pure projective resolutions can be constructed for unbounded complexes of $R$-modules. We use these to obtain a closed symmetric monoidal structure on the unbounded pure derived category.
Ramification invariants of pure extensions
本文研究赋值域纯扩张的分歧不变量，证明直接单分支情形下扩展迹理想由最小多项式导数生成，戴德金差为其除子闭包，并将结果推广到高次纯扩张及伽罗瓦情形。
In this paper, we investigate the notions of $\mathcal{X}^\bot$-projective, $\mathcal{X}$-injective and $\mathcal{X}$-flat modules and give some characterizations of these modules, where $\mathcal{X}$ is a class of left $R$-modules. We prove that the class of all $\mathcal{X}^\bot$-projective modules is Kaplansky. Further, if the class of all $\mathcal{X}$-projective $R$-modules is closed under direct limits, we show the existence of $\mathcal{X}^\bot$-projective covers and $\mathcal{X}$-injective envelopes over a $\mathcal{X}^\bot$-hereditary ring $R.$ Moreover, we decompose a $\mathcal{X}^\b…
Big pure projective modules over commutative noetherian rings: comparison with the completion
该研究针对交换诺特环上的纯投射模分类问题，利用有限生成数据刻画无限生成直和项，拓展经典理论至无限生成情形，还研究了相关幺半群结构并得到子幺半群结论与实现结果。
The Existence of Relative pure Injective Envelopes
设$\mathcal{S}$是一类可表示的$R$ -模，使得$R\in \mathcal{S}$和$\mathcal{S}$有一个子集$\mathcal{S}^*,$，且对任何$U\in \mathcal{S}$都有一个$U^*\in \mathcal{S}^*$具有$U^*\cong U.$.我们证明了$\mathcal{S}$ -纯内射$R$ -模类是预包络的.作为应用，我们证明了$R$的左整体$\mathcal{S}$ -纯投射维数等于它的左整体$\mathcal{S}$ -纯内射维数.作为我们的主要结果，我们证明了$\mathcal{S}$ -纯内射$R$ -模类实际上是包络的.
We characterize Ding modules and complexes over Ding-Chen rings. We show that over a Ding-Chen ring R, the Ding projective (resp. Ding injective, resp. Ding flat) R-modules coincide with the Gorenstein projective (resp. Gorenstein injective, resp. Gorenstein flat) modules, which in turn are nothing more than modules appearing as a cycle of an exact complex of projective (resp. injective, resp. flat) modules. We prove a similar characterization for chain complexes of R-modules: A complex is Ding projective (resp. Ding injective, resp. Ding flat) if and only if each component is Ding projective …
A generalization of the Pontryagin-Hill theorems to projective modules over Prüfer domains
受阿贝尔群自由度的Pontryagin-Hill准则的启发，我们研究了投射模的升链的并又是投射的条件.这些准则的几个扩展被证明为任意环和域上的模，包括一个真正的推广希尔定理的投射模在Prüfer域与可数数量的极大理想。更确切地说，我们证明，在这样的域，模是可数上升链的联盟投射，纯子模也是投射。
F-thresholds of graded rings
a-不变量、F-纯阈值和对角F-阈值是分次K-代数的三个重要不变量。Hirose，Watanabe和Yoshida对强F-正则环的这些不变量建立了关系.在本文中，我们证明了这些关系仅在代数是F-纯的假设下成立。此外，我们给出了F-纯Gorenstein分次K-代数的a-不变量在保持F-纯性的正则序列中的一个解释.这个结果是在精神的贝尔蒂尼定理的投影品种。此外，我们显示与投射维数，Castelnuovo-Mumford正则性，和塞尔的条件$S_k$的连接。我们也提出了类似的结果和问题的特征零。
The Mittag-Leffler condition descents via pure monomorphisms
本文澄清了 Raynaud 和 Gruson 关于 Mittag-Leffler 性质经纯单态射下降的证明，并证明纯投射性也经此下降。
The F-pure threshold versus the a-invariant for standard graded rings
本文完成了关于标准分次强F-正则环为Gorenstein的F-纯阈值判据的猜想证明，并将其推广到F-分裂射影簇的截面环，证明基于Proj的几何性质。
In this article, we study certain local cohomology modules over $F$-pure rings. We give sufficient conditions for the vanishing of some Lyubeznik numbers, derive a formula for computing these invariants when the $F$-pure ring is standard graded and, by its means, we provide some new examples of Lyubeznik tables. We study associated primes of certain Ext-modules, showing that they are all compatible ideals. Finally, we focus on properties that Lyubeznik numbers detect over a globally $F$-split projective variety.
The ideal transform of a graded module $M$ is known to compute the module of twisted global sections of the sheafification of $M$ over a relative projective space. We introduce a second description motivated by the relative BGG-correspondence. However, our approach avoids the full BGG-correspondence by replacing the Tate resolution with the computationally more efficient purely linear saturation and the Castelnuovo-Mumford regularity with the often enough much smaller linear regularity. This paper provides elementary, constructive, and unified proofs that these two descriptions compute the (tr…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。