Related papers: Truncations of Ordered Abelian Groups

We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…

In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…

This is brief and hopefully friendly, with basic notions, a few different perspectives, and references with more information in various directions.

Given a reduced abelian $p$-group, we give an upper bound on the Scott complexity of the group in terms of its Ulm invariants. For limit ordinals, we show that this upper bound is tight. This gives an explicit sequence of such groups with…

We study Ehrhart series with coefficients in Abelian group rings. This opens new enumeration applications and unifies earlier variants, in particular, polynomial weighted, $q$-weighted, and equivariant Ehrhart series.

Suppose $G$ is a finite group acting on an Abelian variety $A$ such that the coarse moduli space $A/G$ is smooth. Using the recent classification result due to Auffarth, Lucchini Arteche, and Quezada, we construct an orbifold semiorthogonal…

We study the set of Dedekind cuts over a linearly ordered Abelian group as a structure over the language (0,<,+,-). Moreover, we obtain a simple set of axioms for the universal part of the theory of such structures. Finally, we prove that…

An algebraic deformation theory of coalgebra morphisms is constructed.

We consider two variants of those Abelian groups with all proper strongly invariant subgroups isomorphic and give an in-depth study of their basic and specific properties in either parallel or contrast to the Abelian groups with all proper…

This work is a continuation of what was done in a previous paper and strongly connected to the recent work of U. Abel and I. Rasa [arXiv:1707.00127]

In this survey paper we discuss some recent results and related open questions in additive combinatorics, in particular, questions about sumsets in finite abelian groups.

An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.

We study the structure of infinite discrete sets D definable in expansions of ordered Abelian groups whose theories are strong and definably complete, with particular emphasis on the set D' comprised of differences between successive…

The Jacobian algebras are introduced and their various properties are studied.

We consider compact and connected Abelian group $G$ with a linearly ordered dual. Based on the description of the structure of compact Hankel operators over $G$, generalizations of the classical Kronecker, Hartman, Peller and…

In 2008, the author proposed a version of duality theory for (not necessarily, Abelian) complex Lie groups, based on the idea of using the Arens-Michael envelope of topological algebra and having an advantage over existing theories in that…

The main goal of this paper is to apply the arithmetic method developed in our previous paper \cite{13} to determine the number of some types of subgroups of finite abelian groups.

This very short correction notes a gap in an argument of an earlier paper, and also provides a theorem of similar flavor to the main result of that paper.

In this paper, we describe the structure of finite groups whose element orders or proper (abelian) subgroup orders form an arithmetic progression of ratio $r\geq 2$. This extends the case $r=1$ studied in previous papers \cite{1,8,4}.

We analyze the abstract representations of the groups of rational points of even-dimensional quasi-split special unitary groups associated with quadratic field extensions. We show that, under certain assumptions, such representations have a…