Semiperfect and perfect group rings
tarafından
Kalaycı, Tekgül, author.
Başlık
:
Semiperfect and perfect group rings
Yazar
:
Kalaycı, Tekgül, author.
Yazar Ek Girişi
:
Kalaycı, Tekgül, author.
Fiziksel Tanımlama
:
vii, 42 leaves:+ 1 computer laser optical disc.
Özet
:
In this thesis, we give a survey of necessary and sufficient conditions on a group G and a ring R for the group ring RG to be semiperfect and perfect. A ring R is called semiperfect R/RadR is semisimple and idempotents of R/RadR can be lifted to R. It is given that if RG is semiperfect, so is R. Necessary conditions on G for RG to be semiperfect are also given for some special type of groups. For the sufficient conditions, several types of rings and groups are considered. If R is commutative and G is abelian, a complete characterization is given in terms of the polynomial ring R[X]. A ring R is called left (respectively, right) perfect if R/RadR is semisimple and RadR is left (respectively, right) T-nilpotent. Equivalently, a ring is called left (respectively, right) perfect if R satisfies the descending chain condition on principal right (respectively, left) ideals. By using these equivalent definitions of a perfect ring and results from group theory, a complete characterization of a perfect group ring RG is given in terms of R and G.
Konu Başlığı
:
Group rings
Yazar Ek Girişi
:
Pusat, Dilek
Tüzel Kişi Ek Girişi
:
İzmir Institute of Technology. Mathematics.
Tek Biçim Eser Adı
:
Thesis (Master)--İzmir Institute of Technology: Mathematics.
İzmir Institute of Technology: Mathematics--Thesis (Master).
Elektronik Erişim
:
Library | Materyal Türü | Demirbaş Numarası | Yer Numarası | Durumu/İade Tarihi |
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IYTE Library | Tez | T001253 | QA251.35 .K35 2014 | Tez Koleksiyonu |