Keqin Liu
We introduce the notion of a Hu-Liu prime ideal in the context of left commutative rngs, and establish the contravariant functor from the category of left commutative rngs into the category of topological spaces.
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
In this paper we introduce and investigate top (bi)comodules} of corings, that can be considered as dual to top (bi)modules of rings. The fully coprime spectra of such (bi)comodules attains a Zariski topology, defined in a way dual to that of defining the Zariski topology on the prime spectra of (commutative rings. We restrict our attention in this paper to duo (bi)comodules (satisfying suitable conditions) and study the interplay between the coalgebraic properties of such (bi)comodules and the introduced Zariski topology. In particular, we apply our results to introduce a Zariski topology on …
We introduce a dual Zariski topology on the spectrum of fully coprime $R$-submodules of a given duo module $M$ over an associative (not necessarily commutative) ring $R$. This topology is defined in a way dual to that of defining the Zariski topology on the prime spectrum of $R$. We investigate this topology and clarify the interplay between the properties of this space and the algebraic properties of the module under consideration.
Given a duo module $M$ over an associative (not necessarily commutative) ring $R,$ a Zariski topology is defined on the spectrum $\mathrm{Spec}^{\mathrm{fp}}(M)$ of {\it fully prime} $R$-submodules of $M$. We investigate, in particular, the interplay between the properties of this space and the algebraic properties of the module under consideration.
In previous work, the second author introduced a topology, for spaces of irreducible representations, that reduces to the classical Zariski topology over commutative rings but provides a proper refinement in various noncommutative settings. In this paper, a concise and elementary description of this refined Zariski topology is presented, under certain hypotheses, for the space of simple left modules over a ring R. Namely, if R is left noetherian (or satisfies the ascending chain condition for semiprimitive ideals), and if R is either a countable dimensional algebra (over a field) or a ring who…
On the Zariski topology on endomorphism monoids of omega-categorical structures
研究ω-范畴结构的内射monic的扎里斯基拓扑与点wise收敛拓扑的一致性，揭示了两种拓扑在特定结构下的差异并解答了相关问题。
Here we continue to characterize a recently introduced notion, le-modules $_{R}M$ over a commutative ring $R$ with unity \cite{Bhuniya}. This article introduces and characterizes Zariski topology on the set $Spec(M)$ of all prime submodule elements of $M$. Thus we extend many results on Zariski topology for modules over a ring to le-modules. The topological space Spec(M) is connected if and only if $R/Ann(M)$ contains no idempotents other than $\overline{0}$ and $\overline{1}$. Open sets in the Zariski topology for the quotient ring $R/Ann(M)$ induces a base of quasi-compact open sets for the …
We study the Zariski topology of the ind-groups of polynomial and free associative algebras $\Aut(K[x_1,...,x_n])$ (which is equivalent to the automorphism group of the affine space $\Aut(K^n))$) and $\Aut(K< x_1,..., x_n>$ via $\Ind$-schemes, toric varieties, approximations and singularities. We obtain some nice properties of $\Aut(\Aut(A))$, where $A$ is polynomial or free associative algebra over a field $K$. We prove that all $\Ind$-scheme automorphisms of $\Aut(K[x_1,...,x_n])$ are inner for $n\ge 3$, and all $\Ind$-scheme automorphisms of $\Aut(K< x_1,..., x_n>)$ are semi-inner. We also …
Automatic continuity, unique Polish topologies, and Zariski topologies on monoids and clones
本文研究幺半群代数结构对相容拓扑的决定作用，证明多种著名幺半群具有自动连续性，并刻画其唯一Polish半群拓扑及Zariski拓扑。
We study Zariski-like topologies on a proper class $X\varsubsetneqq L$ of a complete lattice $\mathcal{L}=(L,\wedge ,\vee ,0,1)$. We consider $X$ with the so called classical Zariski topology $(X,τ^{cl})$ and study its topological properties (e.g. the separation axioms, the connectedness, the compactness) and provide sufficient conditions for it to be $\textit{spectral}$. We say that $\mathcal{L}$ is $X$\emph{-top} iff% \begin{equation*} τ:=\{X\backslash V(a)\mid a\in L\},\text{ where }V(a)=\{x\in L\mid a\leq x\} \end{equation*}% is a topology. We study the interplay between the \textit{algebr…
We extend the Zariski topology on simp A, the finite dimensional simple A-representations, to a non-commutative topology (in the sense of Fred Van Oystaeyen) on rep A, all finite dimensional A-representations, using Jordan-Holder filtrations. The non-commutativity of the topology is enforced by the order of the composition factors.
Let R be an associative ring with identity. We study an elementary generalization of the classical Zariski topology, applied to the set of isomorphism classes of simple left R-modules (or, more generally, simple objects in a complete abelian category). Under this topology the points are closed, and when R is left noetherian the corresponding topological space is noetherian. If R is commutative (or PI, or FBN) the topology is equivalent to the Zariski topology, and when R is the first Weyl algebra (in characteristic zero) we obtain a one-dimensional irreducible noetherian topological space. Com…
Using a Zariski topology associated to a finite field extensions, we give new proofs and generalize the primitive and normal basis theorems.
Several topologies can be defined on the prime, the maximal and the minimal prime spectra of a commutative ring; among them, we mention the Zariski topology, the patch topology and the flat topology. By using these topologies, Tarizadeh and Aghajani obtained recently new characterizations of various classes of rings: Gelfand rings, clean rings, absolutely flat rings, $mp$ - rings,etc. The aim of this paper is to generalize some of their results to quantales, structures that constitute a good abstractization for lattices of ideals, filters and congruences. We shall study the flat and the patch …
An algebraic geometry of paths via the iterated-integrals signature
本文在路径空间上引入Zariski拓扑，利用非结合半洗牌研究满足特定多项式方程的路径簇，揭示了其在路径停止与拼接下的稳定性，并推广了经典代数簇。
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。