논문KCI 등재
Cohomology groups of radical extensions
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Abstract
If k is a subeld ofQ(εm ) then the cohomology group H 2(k(εn )/k) is isomorphic to H 2(k(εn .)/k) with gcd(m,n.) = 1. This enablesus to reduce a cyclotomic k-algebra over k(εn ) to the one over k(εn .).A radical extension in projective Schur algebra theory is regarded as ananalog of cyclotomic extension in Schur algebra theory. We w il studya reduction of cohomology group of radical extension and sho w that aGalois cohomology group of a radical extension is isomorphi c to that of acertain subextension of radical extension. We then draw a cohomologicalcharacterization of radical group.
참고문헌 (10)
- "Projective Schur algebras of nilpotent ype are Brauer equi valent o radicalalgebras"
- "Cohomological methods in group theory" (1972), Marcel Deker Inc
- "Crosed product algebras over cyclotomic extension elds"
- "The crosed product heorem for projective Schur algebras"
- "The Schur group of cyclotomic elds" (1975)
- "Projective representations of nite groups COHOMOLOGY GROUPS OF RADICAL EXTENSIONS 167", mo(graphs and textboksin pure and aplied mathematics) (1985), Marcel Deker Inc
- "Monographs and Textboks in Pure and Aplied Mathematics", Marcel Deker Inc
- "Einfache Algebren und projektive Darstelungen ¨uberZahlk¨orpern" (1978)
- "Cohomology of groups" (1969), Academic press
- "The Schur subgroup of the Brauer group" (1974), Springer-Verlag
관련 논문AI추천
The first cohomology group of units of some real biquadratic number fieldsSAID EL MADRARI장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2025 · 제28권 제3호On the Sum of Two Radical ClassesM. Aslam, M.Zulfiqar경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2003 · 제43권 제4호Galois groups of modules and inverse polynomial modules박상원, 정진선대한수학회 · 대한수학회보2007 · 제44권 제2호Corestriction map on Brauer subgroupsEunmi Choi대한수학회 · 대한수학회논문집2005 · 제20권 제1호A generalization of the Jacobson radicalA. H. Yamini, A. R. Naghipour대한수학회 · 대한수학회보2004 · 제41권 제4호Cohomology and trivial Gottlieb groups이기영대한수학회 · 대한수학회논문집2006 · 제21권 제1호
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