Kubota T.'s An elementary theory of Eisenstein series PDF

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4 The bideterminant function The development of linear algebra over semirings certainly requires such an important matrix invariant as the determinant function, see [38]. It turns out that the determinant cannot be defined in a classical way even for matrices over commutative semirings without zero divisors. The main problem is connected with the fact that if a semiring is not a ring, then there are elements which do not possess additive inverses. 1 below) which has been known since 1972; see also [49] and [36, 38, 41, 57].

Pierce. Linear preserver problems. Amer. Math. Monthly, 108(7):591–605, 2001. -K. Li and N. K. Tsing. Linear preserver problems: a brief introduction and some special techniques. , 162–164:217–235, 1992. [52] M. Marcus and F. May. On a theorem of I. Schur concerning matrix transformations. Arch. , 11:401–404, 1960. [53] G. Mikhalkin. Real algebraic curves, the moment map and amoebas. Ann. of Math. (2), 151(1):309–326, 2000. [54] H. Minc. Permanents. , 1978. [55] S. Pierce et al. A survey of linear preserver problems.

Kim. Boolean Matrix Theory and Applications, volume 70 of Pure and Applied Mathematics. Marcel Dekker, New York, 1982. [48] V. N. Kolokol’tsov and V. Maslov. Idempotent Analysis and Applications. Kluwer, Dordrecht, 1997. Rank and determinant functions for matrices over semirings 33 [49] J. Kuntzmann. Th´eorie des r´eseaux (graphes). Dunod, Paris, 1972. -K. Li and S. Pierce. Linear preserver problems. Amer. Math. Monthly, 108(7):591–605, 2001. -K. Li and N. K. Tsing. Linear preserver problems: a brief introduction and some special techniques.

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