Narrow Class Group
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In algebraic number theory, the narrow class group of a number field K is a refinement of the class group of K that takes into account some information about embeddings of K into the field of real numbers. Suppose that K is a finite extension of Q. Recall that the ordinary class group of K is defined to be C_K = I_K / P_K,,! where IK is the group of fractional ideals of K, and PK is the group of principal fractional ideals of K, that is, ideals of the form aOK where a...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In algebraic number theory, the narrow class group of a number field K is a refinement of the class group of K that takes into account some information about embeddings of K into the field of real numbers. Suppose that K is a finite extension of Q. Recall that the ordinary class group of K is defined to be C_K = I_K / P_K,,! where IK is the group of fractional ideals of K, and PK is the group of principal fractional ideals of K, that is, ideals of the form aOK where a is a unit of K. The narrow class group is defined to be the quotient C_K^+ = I_K / P_K^+.
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