NECESSARY AND SUFFICIENT CONDITIONS FOR UNIQUE FACTORIZATION IN ℤ[(-1 + √<i>d</i>)/2]

DOI10.2206/kyushujm.77.121OpenAlexW4387656388MaRDI QIDQ6091037

Víctor Julio Ramírez Viñas

Publication date: 23 November 2023

Published in: Kyushu Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2206/kyushujm.77.121

zbMATH Keywords

class numberirreducibleprimeunique factorization domainprime-producing polynomials

Mathematics Subject Classification ID

Quadratic extensions (11R11) Quadratic and bilinear Diophantine equations (11D09) Primes represented by polynomials; other multiplicative structures of polynomial values (11N32) Divisibility and factorizations in commutative rings (13A05)

Cites Work

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• Continued fractions and Gauss class number problem for real quadratic fields
• Pell-type equations and class number of the maximal real subfield of a cyclotomic field
• Class number one problem for the real quadratic fields \(\mathbb{Q}(\sqrt{m^2+2r})\)
• A complete determination of the complex quadratic fields of class-number one
• The class number one problem for the real quadratic fields $\mathbb {Q}(\sqrt {(an)^2+4a})$
• A new proof of the Unique Factorization of Z 1 + -d 2 for d = 3, 7, 11, 19, 43, 67, 163
• On a criterion for the class number of a quadratic number field to be one
• Prime-Producing Quadratics
• The Little Book of Bigger Primes
• A NOTE ON CERTAIN REAL QUADRATIC FIELDS WITH CLASS NUMBER UP TO THREE
• A simple criterion for the class number of a quadratic number field to be one

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