Factorization in Integral Domains and in Polynomial Rings

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

Chapter Chapter 6 in Basic Modern Algebra with Applications, 2014, pp 237-255 from Springer

Abstract: Abstract Chapter 6 extends to rings the concepts of divisibility, greatest common divisor, least common multiple, division algorithm, and Fundamental Theorem of Arithmetic for integers with the help of theory of ideals. The main aim of this chapter is to study the problem of factoring the elements of an integral domain as products of irreducible elements. The polynomial rings over a certain class of important rings are studied and the Eisenstein irreducibility criterion, and the Gauss Lemma are proved and related topics are discussed. The study culminates in proving the Gauss Theorem, which provides an extensive class of uniquely factorizable domains.

Keywords: Arbitrary Integral Domain; Polynomial Ring; Eisenstein's Criterion; Unique Factorization Domain (UFD); Important Rings (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-81-322-1599-8_6

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