Coherent and precoherent operators

In this thesis we introduce and investigate new classes of operators which we call coherent and precoherent operators. These operators appear as solutions of some problems in the literature, but they also represent a generalization of some frequently studied classes of operators. After we study different properties of these new classes, we continue by considering a few interesting problems in operator theory. We consider problems about the Moore-Penrose inverse and arbitrary reflexive inverse of the sum of operators, range additivity of operators, lattice properties of the star and core partial orders on Hilbert space operators, the connection about the parallel sum of operators and their infimum in different partial orders, and one special type of operators, inspired by recently introduced disjoint range operators. Accordingly, we generalize and improve a number of results from the existing literature. One part of the thesis is dedicated to Rickart *-rings and generalizations of some presented results in the algebraic setting. We included a number of examples in order to demonstrate our statements and their possible extent: reduction of conditions, proving opposite directions, etc. In the end, we propose few problems for further research on these topics

A*-algebras and Minimal Ideals in Topological Rings

The present thesis mainly concerns B*-algebras, A*-algebras, and minimal ideals in topological rings

Материалы конференции: "Алгебра и математическая логика: теория и приложения"

Сборник содержит тезисы докладов, представленных на международную конференцию "Алгебра и математическая логика: теория и приложения" ( г. Казань 2-6 июня 2014 год) и сопутствующую молодежную летнюю школу "Вычислимость и вычислимые структуры", посвященную 210-летию Казанского университета, 80-летию со дня основания кафедры алгебры (ныне кафедры алгебры и математической логики) Казанского университета Н.Г. Чеботаревым и 70-летию со дня рождения зав. кафедрой члена-корреспондента АН РТ М.М. Арсланова.17

Representing finitely generated refinement monoids as graph monoids

Graph monoids arise naturally in the study of non-stable K-theory of graph C*-algebras and Leavitt path algebras. They play also an important role in the current approaches to the realization problem for von Neumann regular rings. In this paper, we characterize when a finitely generated conical refinement monoid can be represented as a graph monoid. The characterization is expressed in terms of the behavior of the structural maps of the associated I-system at the free primes of the monoid.Both authors are partially supported by the DGI-MINECO and European Regional Development Fund, jointly, through Project MTM2014-53644-P. The second author was partially supported by PAI III grant FQM-298 of the Junta de Andalucía