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Groebner bases for submodules of Z^n
No full textWe define Gr ̈bner bases for submodules of Zn and
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characterize minimal and reduced bases combinatorially in terms
of minimal elements of suitable partially ordered subsets of Zn .
Then we show that Gr ̈bner bases for saturated pure binomial
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ideals of K[x1 , . . . , xn ], char (K) = 2, can be immediately de-
rived from Gr ̈bner bases for appropriate corresponding submod-
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ules of Zn . This suggests the possibility of calculating the Gr ̈bner
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bases of the ideals without using the Buchberger algorith
On the coordinate ring of pairs of alternating matrices with product zero
No full textGiven an integer n ≥ 2, let X and Y be two generic alternating n × n matrices over a commutative ring k. Denote by k[X, Y ] the polynomial ring with indeterminates the entries of X and Y . Moreover denote by I(XY) the ideal generated by the entries of the product of X and Y . The ring k[X, Y ]/I(XY) is the coordinate ring of the variety of pairs (U, V) of alternating n × n matrices with entries in k, such that UV = 0. In this note we give a k-basis of that coordinate
ring, under the assumption that n! is a unit in k. We use some ideas of De Concini, Procesi and Strickland
Novalis, Die Christenheit oder Europa. Ein Fragment; Fichte-Studien; Freiberger naturwissenschaftliche Studien
No full textSwedenborg, Emanuel, Arcana coelestia, quae in Scriptura sacra, seu Verbo Domini sunt, detecta...
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Otto, Rudolf, Das Heilige. Über das Irrationale in der Idee des Göttlichen und sein Verhältnis zum Rationalen
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