000			02148nam a2200229Ia 4500
008			160627s1996||||xx |||||||||||||| ||und||
080			_aUNM Th 89
100			_aManisha, V. Kulkarni _eauthor
245			_aExplicit integral Galois Module structure for low degree abelian extensions
260			_c1996
300			_avi; 42p.
502			_a1996
502			_bPh.D
502			_cUniversity of Madras
520	3		_a'Let M be a finite abelian extension of of Q. Then the ring of integers OM of M is a free, rank one module over the associated order AM/Q'. There is no method for constructing a Z(G) basis for OM when OM is free over Z(G). In this thesis Z(G) basis of OM over L is found whenever extension is tamely ramified, in the cases(i) when M, a bicyclic biquadratic extension of Q and L, quadratic subfield; (ii) M, a cyclic quartic, Galois extension of Q and L, quadratic subfield are considered for the explicit Galois Module Structure Problem. A Field extension M over L is considered where M is a quartic Galois extension of Q and L, it's quadratic subfield. The explicit structure of the associated order is given and conditions under which the ring of integers of M will be free over AM/L as a module and whenever it is free, a generator of OM over AM/L is given. Also the structure of OM as a Z(G) module is studied whenever M is tame over L. It is found explicitly the associated order and the structure of OM as an AM/L- for two different cases, when L = Q(w), G = Z3 where w is a primitive cube root of unity; L = Q(i),M = L [4 Sq.Rt(a)] where i^2 = -1, and a is an integer which is fourth power free. Chapter 4 considers the field extension F of K where K = Q(i) and G = Z4. An integral basis of F over K is found and with this the explicit structure of AF/K and of OF as an AF/K Module. In each of the cases the author gives generator of OF over AF/K.
650	1	4	_aMathematics
653	1	0	_aGalois Module Structure
720	1		_aBalasubramanian, R. _eThesis advisor [ths]
856			_uhttp://www.imsc.res.in/xmlui/handle/123456789/113
942			_2THESIS98 _cTHESIS
999			_c48803 _d48803