Finite dimensional completions in Noether lattices
Johnny Johnson (1975)
Fundamenta Mathematicae
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Johnny Johnson (1975)
Fundamenta Mathematicae
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Johnny Johnson (1971)
Fundamenta Mathematicae
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Johnson, E.W., Johnson, Johnny A., Taylor, Monty B. (2001)
International Journal of Mathematics and Mathematical Sciences
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J. Johnson (1970)
Fundamenta Mathematicae
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J. Johnson (1970)
Fundamenta Mathematicae
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David Whitman (1971)
Fundamenta Mathematicae
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Delany, J.E. (1972)
Portugaliae mathematica
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Johnson, E.W., Johnson, Johnny A., Taylor, Monty B. (1994)
International Journal of Mathematics and Mathematical Sciences
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Yuichi Futa, Yasunari Shidama (2016)
Formalized Mathematics
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In this article, we formalize the definition of lattice of ℤ-module and its properties in the Mizar system [5].We formally prove that scalar products in lattices are bilinear forms over the field of real numbers ℝ. We also formalize the definitions of positive definite and integral lattices and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [14], and cryptographic systems with lattices [15] and coding...
D. Anderson, A. Boals, E. Johnson (1981)
Fundamenta Mathematicae
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M. Janowitz (1970)
Fundamenta Mathematicae
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Johnny Johnson (1975)
Fundamenta Mathematicae
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