The Integral Extension of Isometries of Quadratic Forms Over Local Fields
1966 ◽
Vol 18
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pp. 920-942
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Keyword(s):
Let F be a local field with ring of integers 0 and prime ideal π0. If V is a vector space over F, a lattice L in F is defined as an 0-module in the vector space V with the property that the elements of L have bounded denominators in the basis for V. If V is, in addition, a quadratic space, the lattice L then has a quadratic structure superimposed on it. Two lattices on V are then said to be isometric if there is an isometry of V that maps one onto the other.In this paper, we consider the following problem: given two elements, v and w, of the lattice L over the regular quadratic space V, find necessary and sufficient conditions for the existence of an isometry on L that maps v onto w.
1970 ◽
Vol 22
(2)
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pp. 297-307
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2016 ◽
Vol 59
(3)
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pp. 528-541
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2018 ◽
Vol 33
(2)
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pp. 307
1993 ◽
Vol 114
(1)
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pp. 111-130
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1980 ◽
Vol 87
(3)
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pp. 383-392
1980 ◽
Vol 30
◽
pp. 129-139
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2011 ◽
Vol 84
(2)
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pp. 238-254
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