The Structure of Unit Groups
نویسنده
چکیده
Since the time of ancient Greece and India, Pell’s equation, a2 − db2 = 1, has been studied and its solutions sought after. These solutions are significant, because they correspond to the units of the rings Z[ √ d]. Along with prime numbers, units are vital in understanding the structure and especially the factorization within different rings. Dirichlect’s Unit Theorem establishes the structure of the units of a number field as a finite abelian group. In addition to describing the nature of units, Dirichlect’s Unit Theorem represents the interconnectedness of geometry (namely Minkowski’s Theorem), algebra, and number theory.
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تاریخ انتشار 2014