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2000 | 83 | 1 | 43-53
Tytuł artykułu

Hermitian and quadratic forms over local classical crossed product orders

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let R be a complete discrete valuation ring with quotient field K, L/K be a Galois extension with Galois group G and S be the integral closure of R in L. If a is a factor set of G with values in the group of units of S, then (L/K,a) (resp. Λ =(S/R,a)) denotes the crossed product K-algebra (resp. crossed product R -order in A). In this paper hermitian and quadratic forms on Λ -lattices are studied and the existence of at most two irreducible non-singular quadratic Λ -lattices is proved (Theorem 3.5). Further the orthogonal decomposition of an arbitrary non-singular quadratic Λ -lattice is given.
Słowa kluczowe
Rocznik
Tom
83
Numer
1
Strony
43-53
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-11-10
poprawiono
1999-08-04
Twórcy
autor
  • Department of Civil Engineering, University of Thessaly, Pedion Areos, Volos 383 34, Greece
  • Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54 006, Greece
Bibliografia
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  • [C-R] C. Curtis and I. Reiner, Methods of Representation Theory, Vol. I, Wiley, 1981.
  • [Ch-Th] A. Chalatsis and Th. Theohari-Apostolidi, Maximal orders containing local crossed products, J. Pure Appl. Algebra 50 (1988), 211-222.
  • [G-R] E. L. Green and I. Reiner, Integral representations and diagrams, Michigan Math. J. 25 (1978), 53-84.
  • [H-Th] Y. Hatzaras and Th. Theohari-Apostolidi, Involutions on classical crossed products, Comm. Algebra 24 (1996), 1003-1016.
  • [Kel] G. M. Kelly, On the radical of a category, J. Austral. Math. Soc. 4 (1964), 299-307.
  • [Kn] M. A. Knus, Quadratic and Hermitian Forms over Rings, Grudlehren Math. Wiss. 294, Springer, Berlin 1991.
  • [Q] H.-G. Quebbemann, Zur Klassifikation unimodularer Gitter mit Isometrie von Primzahlordnung, J. Reine Angew. Math. 326 (1981), 158-170.
  • [Q-S-S] H.-G. Quebbemann, W. Scharlau and M. Shulte, Quadratic and Hermitian forms in additive and abelian categories, J. Algebra 59 (1979), 264-289.
  • [Re] I. Reiner, Maximal Orders, Academic Press, 1975.
  • [Ri] C. Riehm, Hermitian forms over local hereditary orders, Amer. J. Math. 106 (1984), 781-800.
  • [R-R] C. M. Ringel and K. W. Roggenkamp, Diagrammatic methods in the representation theory of orders, J. Algebra 60 (1979), 11-42.
  • [Sch] W. Scharlau, Quadratic and Hermitian Forms, Grudlehren Math. Wiss. 270, Springer, Berlin, 1985.
  • [Sim] D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra Logic Appl. 4, Gordon & Breach, 1992.
  • [Th] Th. Theohari-Apostolidi, Local crossed product orders of finite representation type, J. Pure Appl. Algebra 41 (1986), 87-98.
  • [Th-W] Th. Theohari-Apostolidi and A. Wiedemann, Integral representaions of local crossed products of finite type, Bayreuther Math. Schriften 40 (1992), 169-176.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv83i1p43bwm
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