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Isomorphism Theorems for Basic Constructive Algebraic Structures with Special Emphasize On Constructive Semigroups with Apartness—An Overview

  • Melanija MitrovićEmail author
  • Sergei Silvestrov
Conference paper
  • 36 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 317)

Abstract

This overview is an introduction to the basic constructive algebraic structures with apartness with special emphasises on a set and semigroup with apartness. The main purpose of this paper, inspired by Bauer [2], is to make some sort of understanding of constructive algebra in Bishop’s style position for those (classical) algebraists as well as for the ones who apply algebraic knowledge who might wonder what is constructive algebra all about. Every effort has been made to produce a reasonably prepared text with such definite need. In the context of basic constructive algebraic structures constructive analogous of isomorphism theorems will be given. Following their development, two points of view on a given subject: classical and constructive will be considered. This overview is not, of course, a comprehensive one.

Keywords

Sets with apartness Groups and rings with tight apartness Semigroups with apartness Apartness isomorphism theorems 

MSC 2010 Classification

20M15 03F65 03D45 

Notes

Acknowledgements

Melanija Mitrović is financially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, Grant 174026, and by the Faculty of Mechanical Engineering, University of Niš, Serbia, Grant “Research and development of new generation machine systems in the function of the technological development of Serbia”. Melanija Mitrovicć is grateful to Mathematics and Applied Mathematics Research Environment MAM, Division of Applied Mathematics at the School of Education, Culture and Communication at Mälardalen University for cordial hospitality and excellent environment for research and cooperation during her visit.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsFaculty of Mechanical Engineering, University of NišNišSerbia
  2. 2.Division of Applied Mathematics, School of Education, Culture and CommunicationMälardalen UniversityVästeråsSweden

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