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Full-Text Articles in Number Theory
Unique Prime Factorization Of Ideals In The Ring Of Algebraic Integers Of An Imaginary Quadratic Number Field, Nolberto Rezola
Unique Prime Factorization Of Ideals In The Ring Of Algebraic Integers Of An Imaginary Quadratic Number Field, Nolberto Rezola
Electronic Theses, Projects, and Dissertations
The ring of integers is a very interesting ring, it has the amazing property that each of its elements may be expressed uniquely, up to order, as a product of prime elements. Unfortunately, not every ring possesses this property for its elements. The work of mathematicians like Kummer and Dedekind lead to the study of a special type of ring, which we now call a Dedekind domain, where even though unique prime factorization of elements may fail, the ideals of a Dedekind domain still enjoy the property of unique prime factorization into a product of prime ideals, up to order …
A Fundamental Unit Of O_K, Susana L. Munoz
A Fundamental Unit Of O_K, Susana L. Munoz
Electronic Theses, Projects, and Dissertations
In the classical case we make use of Pells equation to compute units in the ring OF. Consider the parallel to the classical case and the quadratic field extension that creates the ring OK. We use the generalized Pell's equation to find the units in this ring since they are solutions. Through the use of continued fractions we may further characterize this ring and compute its units.