Rings: Introductory Concepts

Mahima Ranjan Adhikari and Avishek Adhikari
Additional contact information
Mahima Ranjan Adhikari: Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC)
Avishek Adhikari: University of Calcutta, Department of Pure Mathematics

Chapter Chapter 4 in Basic Modern Algebra with Applications, 2014, pp 159-201 from Springer

Abstract: Abstract Rings also serve as a fundamental building blocks for modern algebra. Chapter 4 introduces the concept of rings, another fundamental concept in the study of modern algebra. A group is endowed with only one binary operation while a ring is endowed with two binary operations connected by some interrelations. Fields form a very important class of rings. The concept of rings arose through the attempts to prove Fermat’s last theorem and was initiated by Richard Dedekind (1831–1916) around 1880. David Hilbert (1862–1943) coined the term “ring”. Emmy Noether (1882–1935) developed the theory of rings under his guidance. A very particular but important type of rings known as commutative rings plays an important role in algebraic number theory and algebraic geometry. On the other hand, non-commutative rings are used in non-commutative geometry and quantum groups. In this chapter Wedderburn theorem on finite division rings, and some special rings, such as rings of power series, rings of polynomials, rings of continuous functions, rings of endomorphisms of abelian groups and Boolean rings are also studied.

Keywords: Integral Domain; Formal Power Series; Division Ring; Endomorphism Ring; Ring Homomorphism (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-1599-8_4

Ordering information: This item can be ordered from
http://www.springer.com/9788132215998

DOI: 10.1007/978-81-322-1599-8_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().