Related papers: How to Expand the Zariski Topology

The mod-2 arithmetic Milnor invariants, introduced by Morishita, provide a decomposition law for primes in canonical Galois extensions of $\mathbb{Q}$ with unitriangular Galois groups, and contain the Legendre and Redei symbols as special…

Let $V(I)$ be a polarized projective variety or a subvariety of a product of projective spaces and let $A$ be its (multi-)homogeneous coordinate ring. Given a full-rank valuation $\mathfrak v$ on $A$ we associate weights to the coordinates…

We prove several extension theorems for Roumieu ultraholomorphic classes of functions in sectors of the Riemann surface of the logarithm which are defined by means of a weight function or weight matrix. Our main aim is to transfer the…

In 1979, Vogan proposed a generalised $\tau$-invariant for characterising primitive ideals in enveloping algebras. Via a known dictionary this translates to an invariant of left cells of finite Weyl groups. Although it is not a complete…

We define a functor $\rr^\ast$ from the category of positively determined modules to the category of squarefree modules which plays the role of passing from a monomial ideal to its radical. By using this functor, we generalize several…

Let R be a commutative ring with identity and M be an R-module. A proper ideal I of R is said to be a $z^\circ$-ideal if for each $a \in I$ the intersection of all minimal prime ideals containing a is contained in I. The purpose of this…

We study (two-sided) ideals $I$ in the enveloping algebra $\U(\frak g_\infty)$ of an infinite-dimensional Lie algebra $\frak g_\infty$ obtained as the union (equivalently, direct limit) of an arbitrary chain of embeddings of simple…

Completely prime right ideals are introduced as a one-sided generalization of the concept of a prime ideal in a commutative ring. Some of their basic properties are investigated, pointing out both similarities and differences between these…

We derive several tools for classifying tensor ideals in monoidal categories. We use these results to classify tensor ideals in Deligne's universal categories RepO, RepGL and RepP. These results are then used to obtain new insight into the…

We present an efficient method to compute the modular extension of both fermionic topological orders and $\mathbb{Z}_2$-symmetric bosonic topological orders in two spatial dimensions, basing on congruence representations of…

We develop the theory of topological radicals in Banach Lie algebras, consider various ways of constructing such radicals and study a family of (pre)radicals related to subalgebras and ideals of finite codimension in Banach Lie algebras. It…

Some descriptions of linked ideals in a commutative Notherian ring $R$ are provided in terms of the Associated prime ideals of $R$. Then, among other things, we make some characterization of Cohen-Macaulay, Gorenstein and regular local…

Associated to each Tambara functor $T$ is its Nakaoka spectrum $\mathrm{Spec}(T)$, analogous to the Zariski spectrum of a commutative ring. We establish that this topological space is spectral. This result follows from an analysis of the…

We introduce and study the notion of ramification ideals in higher ramification theory. After general results on their computation, we discuss their connection with defect and compute them for Artin-Schreier extensions and Kummer extensions…

Let k and n be positive even integers. For a cuspidal Hecke eigenform g in the Kohnen plus subspace of weight k-n/2+1/2 and level 4, let I(g) be the Duke-Imamoglu-Ikeda lift of g in the space of cusp forms of weight k for Sp(n,Z), and f the…

In this paper we study initial topological properties of the (non-)finitely-generated locus of Frobenius Algebra coming from Stanley-Reisner rings defined through face ideals. More specifically, we will give a partial answer to a conjecture…

We show that the restriction functor from oriented factor planar algebras to subfactor planar algebras admits a left adjoint, which we call the free oriented extension functor. We show that for any subfactor planar algebra realized as the…

In this paper, we define the concepts of r-hyperideal and n-hyperideal of the multiplicative hyperring R which are two new classes of hyperideals. Several properties of them are provided.

In the first part of this paper we investigate the operator aspect of higher-rank supersymmetric model which is introduced as a Lie theoretic extension of the $N=2$ minimal model with the simplest case $su(2)$ corresponding to the $N=2$…

We introduce the class of split regular Hom-Lie superalgebras as the natural extension of the one of split Hom-Lie algebras and Lie superalgebras, and study its structure by showing that an arbitrary split regular Hom-Lie superalgebra…