finitely generated extension

finitely generated extension

[¦fī‚nīt·lē ¦gen·ə‚rād·əd ik′sten·chən]
(mathematics)
A finitely generated extension of a field k is the smallest field which contains k and some finite set of elements.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Let K be a number field, and R be a finitely generated extension ring of Z in K.