Titlebook: Combinatorial Methods; Free Groups, Polynom Alexander A. Mikhalev,Vladimir Shpilrain,Jie-Tai Y Book 2004 Springer Science+Business Media Ne

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巧思

Tiago Roux Oliveira,Leonid Fridman,Liu HsuLet . be a field and let .[.] = .[., ... , .] be the polynomial algebra in . variables ., ... , . over .. Sometimes we prefer to denote the elements of . by ., etc. In this chapter, we study the group of .-algebra automorphisms Aut(.[., ... , .]), . ≥ 2.

phytochemicals

Spirometry

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5 Voeding bij kauw- en slikstoornissen,Leibniz algebras are possible non-(anti)commutative analogs of Lie algebras. These algebras have appeared in [55] under the name “D-algebras”. In [221, 222, 223] J.-L. Loday and T. Pirashvili studied these analogs from the point of view of homological algebra.

石墨

The Jacobian ConjectureIn this chapter, we address the most famous of the problems about polynomial mappings: .. If for . polynomials ., ... , . ∈ .[., ... , .], the corresponding Jacobian matrix is invertible, then .[., ... , .] = .[., ... , .].

Ceremony

Nagata’s ProblemLet . be a field and let .[.] = .[., ... , .] be the polynomial algebra in . variables ., ... , . over .. Sometimes we prefer to denote the elements of . by ., etc. In this chapter, we study the group of .-algebra automorphisms Aut(.[., ... , .]), . ≥ 2.

ONYM

The Embedding ProblemLet .[., ... , .] be the polynomial algebra in n variables over a field .. Any collection of polynomials ., ... , . from .[., ... , .] determines an algebraic variety {. = 0, . = 1, ... , .} in the affine space .. We shall denote this algebraic variety by . (., ... , .).

Foreshadow

Coordinate PolynomialsLet . = .[., ... , .] be the polynomial algebra over a field . of characteristic 0. Recall that a polynomial . ∈ . is . if it can be included in a generating set of cardinality . of the algebra ..

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