Related papers: Necklace rings and logarithmic functions

Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…

We show that differential calculus (in its usual form, or in the general form of topological differential calculus) can be fully imdedded into a functor category (functors from a small category of anchord tangent algebras to anchored sets).…

We study factoriality and the class groups of locally acyclic cluster algebras. To do so, we introduce a new class of rings called finite Laurent intersection rings (FLIRs), which includes locally acyclic cluster algebras, full-rank upper…

Let $m,n\in \Bbb{N}$. We represent the additive subgroups of the ring $\Bbb{Z}_m \times \Bbb{Z}_n$, which are also (unital) subrings, and deduce explicit formulas for $N^{(s)}(m,n)$ and $N^{(us)}(m,n)$, denoting the number of subrings of…

We study the ring of algebraic functions on the space of persistence barcodes, with applications to pattern recognition.

An important instance of Rota-Baxter algebras from their quantum field theory application is the ring of Laurent series with a suitable projection. We view the ring of Laurent series as a special case of generalized power series rings with…

It is known that the category of Lie algebras over a ring admits algebraic exponents. The aim of this paper is to show that the same is true for the category of internal Lie algebras in an additive, cocomplete, symmetric, closed, monoidal…

We give a brief introduction to computational algebraic number theory in OSCAR. Our main focus is on number fields, rings of integers and their invariants. After recalling some classical results and their constructive counterparts, we…

We study the algebraic $K$-theory of the ring of continuous functions on a compact Hausdorff space with values in a local division ring, e.g., a local field: We compute its negative $K$-theory and show its $K$-regularity. The complex case…

In this paper, we give an overview of our previous paper concerning the investigation of the algebraic and $p$-adic properties of Eisenstein-Kronecker numbers using Mumford's theory of algebraic theta functions.

In this paper, we define and study the arithmetic of the ring of $\mathbb{U}$-operators for reductive $p$-adic groups. These operators generalise the notion of "successor" operators for trees with a marked end. We show that they are…

Despite the obvious similarities in definitions and properties, the Nagata ring and the Kronecker function ring have been classically treated independently, when the coefficients are not in a Pr\"ufer domain. The purpose of this paper is to…

We develop algorithms to turn quotients of rings of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In addition, we study normal forms for modules over such rings and…

A ring with an Auslander dualizing complex is a generalization of an Auslander-Gorenstein ring. We show that many results which hold for Auslander-Gorenstein rings also hold in the more general setting. On the other hand we give criteria…

We develop a theory of Burnside rings in the context of birational equivalences of algebraic varieties equipped with logarithmic volume forms. We introduce a residue homomorphism and construct an additive invariant of birational morphisms.…

The theory of bisets has been very useful in progress towards settling the longstanding question of determining units for the Burnside ring. In 2006 Bouc used bisets to settle the question for $p$-groups. In this paper, we provide a…

This paper presents an extension of the concept of NR-clean introduced in [12] to graded ring theory. We define and explore graded NR-clean rings, which generalize the class of graded U-nil clean previously studied in [15]. We provide…

The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…

The aim of these notes is to study some of the structural aspects of the ring of arithmetical functions. We prove that this ring is neither Noetherian nor Artinian. Furthermore, we construct various types of prime ideals. We also give an…

We establish several new $\Omega$-theorems for logarithmic derivatives of the Riemann zeta function and Dirichlet $L$-functions. In particular, this improves on earlier work of Landau (1911), Bohr-Landau (1913), and recent work of Lamzouri.