On rings of integers of relative abelian extensions of number fields

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On rings of integers of relative abelian extensions of number fields

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dc.contributor.author Venkataraman, S.
dc.date.accessioned 2009-08-11T11:43:25Z
dc.date.available 2009-08-11T11:43:25Z
dc.date.issued 2009-08-11T11:43:25Z
dc.date.submitted 1992
dc.identifier.uri http://hdl.handle.net/123456789/65
dc.description.abstract By a number field, we mean a finite extension of Q. If F is a number field, the ring of integers of F is the integral closure of Z in F. Since the ring of integers of F is finitely generated and torsion free, it is free over Z. So Z-basis exists. To find the conditions for the existence of extension of number fields, and to compute it explicitly when it exists is an interesting problem in algebraic number theory. Mann's theorem is used in this thesis, for the discussions of problems in two particular types of integral bases. This thesis is dealing with the study of two problems (viz., Problem of Galois Module Structure, and a Problem with respect to Monogeneity), for two families of abelian extensions. en_US
dc.publisher.publisher
dc.subject Elliptic Functions en_US
dc.subject Modular Functions en_US
dc.subject Field Theory en_US
dc.subject Quadratic Extensions en_US
dc.subject Algebraic Number Theory en_US
dc.title On rings of integers of relative abelian extensions of number fields en_US
dc.type.degree Ph.D en_US
dc.type.institution University of Madras en_US
dc.description.advisor Balasubramanian, R.
dc.description.pages v; 42p. en_US
dc.type.mainsub Mathematics en_US

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