Related papers: Strongly inessential elements of a perfect height …
In this article we fully describe the domain of the infinitesimal generator of the optimal state semigroup which arises in the theory of the linear-quadratic problem for a specific class of boundary control systems. This represents an…
In this paper, we study the strong Lefschetz property of artinian complete intersection ideals generated by products of linear forms. We prove the strong Lefschetz property for a class of such ideals with binomial generators.
The Standard Model of Particle Physics has proven to be tremendously successful as the fundamental theory that describes the elementary particles that compose our Universe, as well as the interactions among them. Despite the countless…
Let $R$ be an affine algebra over an algebraically closed field of characteristic $0$ with dim$(R)=n$. Let $P$ be a projective $A=R[T_1,\cdots,T_k]$-module of rank $n$ with determinant $L$. Suppose $I$ is an ideal of $A$ of height $n$ such…
We first establish a sufficient condition for an additively idempotent semiring to be nonfinitely based. As applications, we exhibit several examples of additively idempotent semirings satisfying this condition, including a $4$-element…
A so-called smart material is a material that is the seat of one or more multiphysical coupling. One of the key points in the development of the constitutive laws of these materials, either at the local or at the global scale, is to…
We study a family of determinantal ideals whose decompositions encode the structural zeros in conditional independence models with hidden variables. We provide explicit decompositions of these ideals and, for certain subclasses of models,…
A recurring theme in finite group theory is understanding how the structure of a finite group is determined by the arithmetic properties of group invariants. There are results in the literature determining the structure of finite groups…
In this paper we consider a norm based on the infinitesimal generator of the shift semigroup in a direction. The relevance of such a focus is guaranteed by an abstract representation of a fractional integro-differential operator by means of…
In SGA 2, Grothendieck conjectures that the \'etale fundamental group of the punctured spectrum of a complete noetherian local domain of dimension at least two with algebraically closed residue field is topologically finitely generated. In…
Suppose that R is a two-dimensional normal standard-graded domain over a finite field. We prove that there exists a uniform Frobenius test exponent b for the class of homogeneous ideals in R generated by at most n elements. This means that…
A homogeneous ideal $I$ of a polynomial ring $S$ is said to have the Rees property if, for any homogeneous ideal $J \subset S $ which contains $I$, the number of generators of $J$ is smaller than or equal to that of $I$. A homogeneous ideal…
The problem of finding generators of the $GL$-ideal of the relations between the generators of the algebra of invariants of the dihedral group acting on $m$-tuples of vectors from its defining $2$-dimensional representation is studied. It…
This article addresses two central problems in the theory of quandle rings. First, motivated by Conjecture 3.10 in Internat. J. Math. 34 (2023), no. 3, Paper No. 2350011: for a semi-latin quandle $X$, every nonzero idempotent in the…
Let $G$ be a group generated by a finite set $A$. An element $g\in G$ is a strict dead end of depth $k$ (with respect to $A$) if $|g|>|ga_1|>|ga_1a_2|>...>|ga_1a_2... a_k|$ for any $a_1,a_2, ..., a_k\in A^{\pm1}$ such that the word…
For a monomial ideal $I$, let $G(I)$ be its minimal set of monomial generators. If there is a total order on $G(I)$ such that the corresponding Lyubeznik resolution of $I$ is a minimal free resolution of $I$, then $I$ is called a Lyubeznik…
Let $K$ be a number field of degree $d$. Then every ideal $I$ in the ring of integers ${\mathcal O}_K$ contains infinitely many primitive elements, i.e. elements of degree $d$. A bound on smallest height of such an element in $I$ follows…
The strong global dimension of a ring is the supremum of the length of perfect complexes that are indecomposable in the derived category. In this note we characterize the noetherian commutative rings that have finite strong global…
We study ideals generated by $2$--minors of generic Hankel matrices.
In the paper, we study the generator problem of II$_1$ factors. By defining a new concept related to the number of generators of a von Neumann algebra, we are able to show that a large class of II$_1$ factors are singly generated, i.e.,…