Related papers: On $e^*$-topological Rings
This paper aims to provide a careful and self-contained introduction to the theory of topological degree in Euclidean spaces. It is intended for people mostly interested in analysis and, in general, a heavy background in algebraic or…
Infinite loop space theory, both additive and multiplicative, arose largely from two basic motivations. One was to solve calculational questions in geometric topology. The other was to better understand algebraic K-theory. The Adams…
This paper introduces a novel class of topological spaces, termed SC*-regular spaces, which are defined using SC*-open sets. We explore their fundamental properties and examine their connections with existing regularity concepts, such as…
Given a ring R, we investigate tilting modules of the form S \oplus S/R for some injective ring epimorphism R \to S. In particular, we are interested in tilting modules arising from Schofield's universal localization. For some rings, in…
The general theory of Grothendieck categories is presented. We systemize the principle methods and results of the theory, showing how these results can be used for studying rings and modules.
The set of open subsets in a proximity space (X,{\zeta}) forms a topological system that enables the definition of proximal and descriptive topological groups. This framework naturally extends to proximal and descriptive topological rings…
Notions of topological free entropy and of free capacity are introduced in the $C^*$-algebra context. Basic properties, basic problems and connections to potential theory and random matrix theory are discussed.
The object of this paper is the tameness conjecture which describes an arbitrary graded k-algebra homomorphism of polytopal rings. We give further evidence of this conjecture by showing supporting results concerning joins, multiples and…
The purpose of this paper is to formulate a number of conjectures giving a rather complete description of the tautological ring of M_g and to discuss the evidence for these conjectures.
In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivial examples of rings of new defined…
In this paper, we introduce the concept of $S$-B\'ezout ring, as a generalization of B\'ezout ring. We investigate the relationships between $S$-B\'ezout and other related classes of rings. We establish some characterizations of…
This paper aims to study the notion of $e^*\text{-}\theta$-open \cite{Ozkoc1} sets and to investigate new properties of this notion. Also, we define a new type of set, called $e^*\text{-}\theta\text{-}D$-set, via the notion of…
Motivated by algebraic quantum field theory and our previous work we study properties of inductive systems of \ $C^*$-algebras over arbitrary partially ordered sets. A partially ordered set can be represented as the union of the family of…
D. K. Biss (Topology and its Applications 124 (2002) 355-371) introduced the topological fundamental group and presented some interesting basic properties of the notion. In this article we intend to extend the above notion to homotopy…
Recent development of network structure analysis shows that it plays an important role in characterizing complex system of many branches of sciences. Different from previous network centrality measures, this paper proposes the notion of…
In this paper, a theory of quandle rings is proposed for quandles analogous to the classical theory of group rings for groups, and interconnections between quandles and associated quandle rings are explored.
We compute K-theory for ring C*-algebras in the case of higher roots of unity and thereby completely determine the K-theory for ring C*-algebras attached to rings of integers in arbitrary number fields.
We examine the various linkings in space-time of ``ball-like'' and ``ring-like'' topological solitons in certain nonlinear sigma models in 2+1 and 3+1 dimensions. By going to theories where soliton overlaps are forbidden, these linkings…
We associate reduced and full C*-algebras to arbitrary rings and study the inner structure of these ring C*-algebras. As a result, we obtain conditions for them to be purely infinite and simple. We also discuss several examples.…
Gorenstein rings are important to mathematical areas as diverse as algebraic geometry, where they encode information about singularities of spaces, and homotopy theory, through the concept of model categories. In consequence, the study of…