Explicit integral Galois Module structure for low degree abelian extensions (Record no. 48803)
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| 000 -LEADER | |
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| fixed length control field | 02148nam a2200229Ia 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 160627s1996||||xx |||||||||||||| ||und|| |
| 080 ## - UNIVERSAL DECIMAL CLASSIFICATION NUMBER | |
| Universal Decimal Classification number | UNM Th 89 |
| 100 ## - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Manisha, V. Kulkarni |
| Relator term | author |
| 245 ## - TITLE STATEMENT | |
| Title | Explicit integral Galois Module structure for low degree abelian extensions |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Year of publication | 1996 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | vi; 42p. |
| 502 ## - DISSERTATION NOTE | |
| Dissertation note | 1996 |
| 502 ## - DISSERTATION NOTE | |
| Degree Type | Ph.D |
| 502 ## - DISSERTATION NOTE | |
| Name of granting institution | University of Madras |
| 520 3# - SUMMARY, ETC. | |
| Summary, etc | '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 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematics |
| 653 10 - INDEX TERM--UNCONTROLLED | |
| Uncontrolled term | Galois Module Structure |
| 720 1# - ADDED ENTRY--UNCONTROLLED NAME | |
| Thesis Advisor | Balasubramanian, R. |
| Relator term | Thesis advisor [ths] |
| 856 ## - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://www.imsc.res.in/xmlui/handle/123456789/113 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | THESIS & DISSERTATION |
| Withdrawn status | Lost status | Damaged status | Not for loan | Current library | Full call number | Accession Number | Uniform Resource Identifier | Koha item type |
|---|---|---|---|---|---|---|---|---|
| IMSc Library | UNM Th 89 | 66563 | http://www.imsc.res.in/xmlui/handle/123456789/113 | THESIS & DISSERTATION |