Related papers: Strongly inessential elements of a perfect height …
We show that in an essentially small rigid tensor triangulated category with connected Balmer spectrum there are no proper non-zero thick tensor ideals admitting strong generators. This proves, for instance, that the category of perfect…
It has been a well-known fact since Euclid's time that there exist infinitely many rational primes. Two natural questions arise: In which other rings, sufficiently similar to the integers, are there infinitely many irreducible elements? Is…
This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…
The elements of a finite partial order $P$ can be identified with the maximal indecomposable two-sided ideals of its incidence algebra $\A$, and then for two such ideals, $I\prec J \iff IJ \not=0$. This offers one way to recover a poset…
We classify all unmixed monomial ideals I of codimension 2 which are generically a complete intersection and which have the property that the symbolic power algebra A(I) is standard graded. We give a lower bound for the highest degree of a…
Exceptional points are universal level degeneracies induced by non-Hermiticity. Whereas past decades witnessed their new physics, the unified understanding has yet to be obtained. Here we present the complete classification of generic…
This paper introduces the concept of a generating set for stochastic matrices -- a subset of matrices whose repeated composition generates the entire set. Understanding such generating sets requires specifying the "indivisible elements" and…
This paper is concerned with determining the number of generators in each degree for minimal sets of homogeneous generators for saturated ideals defining fat point subschemes $Z=m_1p_1+ ... +m_rp_r$ for general sets of points $p_i$ of…
We define the notion of a separable element in a finite Weyl group, generalizing the well-studied class of separable permutations. We prove that the upper and lower order ideals in weak Bruhat order generated by a separable element are…
We show that the number of elements generating a squarefree monomial ideal up to radical can always be bounded above in terms of the number of its minimal monomial generators and the maximal height of its minimal primes.
This work presents an example of a finitely presented semigroup $S$ containing an infinite nonnilpotent nil ideal $LS$, whose elements do not have a square (i.e. any word of the type $LXYYZ$ equals zero.)
In this paper, we introduce the concepts of strongly 2-absorbing primary ideals (resp., submodules) and strongly 2-absorbing ideals (resp., submodules) as generalizations of strongly prime ideals. Furthermore, we investigate some basic…
Given a symbolic power of a homogeneous ideal in a polynomial ring, we study the problem of determining which powers of the ideal contain it. For ideals defining 0-dimensional subschemes of projective space, as an immediate corollary of our…
We demonstrate equivalence between two definitions of lower finite highest weight categories. We also show that, in the presence of a duality, a lower finite highest weight structure on a category is unique. Finally, we give a new proof for…
Let R be a differential domain finitely generated over a differential field, F, with field of constants, C, of characteristic 0. Let E be the quotient field of R. The paper investigates necessary and sufficient conditions on R's…
It was shown by Cellini and Papi that an ad-nilpotent ideal determines certain element of the affine Weyl group, and that there is a bijection between the ad-nilpotent ideals and the integral points of a simplex with rational vertices. We…
A subset S of a group G invariably generates G if G = <s^(g(s)) | s in S> for each choice of g(s) in G, s in S. In this paper we study invariable generation of infinite groups, with emphasis on linear groups. Our main result shows that a…
We introduce the notion of a strong minuscule element, and prove that the dominant integral weight associated to a strong minuscule element is the fundamental weight corresponding to a short simple root. In addition, we enumerate the strong…
Monomial ideals which are generic with respect to either their generators or irreducible components have minimal free resolutions derived from simplicial complexes. For a generic monomial ideal, the associated primes satisfy a saturated…
Following the approach in the book "Commutative Algebra", by D. Eisenbud, where the author describes the generic initial ideal by means of a suitable total order on the terms of an exterior power, we introduce first the generic initial…