Download Advances in number theory: Proc. 3rd conf. of Canadian by Fernando Q. Gouvea, Noriko Yui PDF

By Fernando Q. Gouvea, Noriko Yui

This publication comprises the lawsuits of the 3rd convention of the Canadian quantity conception organization. The 38 technical papers awarded during this quantity speak about correct and well timed concerns within the fields of analytic quantity concept, arithmetical algebraic geometry, and diophantine approximation. The booklet contains numerous papers honoring Paulo Ribenboim, to whom this convention used to be committed.

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O. (1979). Matroid representation over GF(3). J. Comb. Theory Ser. B 26, 159-73. O. (1980). Decomposition of regular matroids. J. Comb. Theory Ser. B 28, 305-60. T. (1958). A homotopy theorem for matroids, I, II. Trans. Am. Math. Soc. 88, 144-74. T. (1959). Matroids and Graphs, Trans. Am. Math. Soc. 90, 527-52. Vamos, P. (1971). A necessary and sufficient condition for a matroid to be linear. Mobius Algebra Conference. University of Waterloo, 166-73. A. (1976). Matroid Theory. Academic Press, London.

A number of matroids have the interesting property that they possess a coordinatization which is universal with respect to such specializations. 2. Proposition. Let M be a unimodular matroid and B a basis of M. Then M has a coordinatization (0 over Z[x l , X2 , ••• , Xn], for appropriate m, which is in echelonform with respect to B, such that every coordinatization ( of M over any field, with ( in echelon form with respect to B, is a specialization of (0. Proof Let (lIA) be any unimodular coordinatization of Mover Z, in echelon form with respect to B.

This provides another interesting special class of matroids, and raises the natural problem of determining when a given matroid M is isomorphic to such an algebraic independence matroid. We assume that M is finite. Thus we say that (: s --+ K is an algebraic representation of M(S) over k if A s;;; S is independent in M if and only if (I ... is injective and ((A) is algebraically independent over k. Equivalently, by restricting our attention to the subfield K' of K generated by (S), an algebraic representation ( of M may also be characterized by: B s;;; S is a basis of M if and only if (IB is injective and (B) is a 24 Neil White transcendence basis of K'jk.

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