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Factorization in Integral Domains and in Polynomial Rings

In: Basic Modern Algebra with Applications

Author

Listed:
  • Mahima Ranjan Adhikari

    (Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC))

  • Avishek Adhikari

    (University of Calcutta, Department of Pure Mathematics)

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.

Suggested Citation

  • Mahima Ranjan Adhikari & Avishek Adhikari, 2014. "Factorization in Integral Domains and in Polynomial Rings," Springer Books, in: Basic Modern Algebra with Applications, edition 127, chapter 0, pages 237-255, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-1599-8_6
    DOI: 10.1007/978-81-322-1599-8_6
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