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A field automorphism of a field F is a bijective map sigma:F->F that preserves all of F's algebraic properties, more precisely, it is an isomorphism. For example, complex ...

An extension field F subset= K is called finite if the dimension of K as a vector space over F (the so-called degree of K over F) is finite. A finite field extension is ...

Also called the Tait flyping conjecture. Given two reduced alternating projections of the same knot, they are equivalent on the sphere iff they are related by a series of ...

A formal power series, sometimes simply called a "formal series" (Wilf 1994), of a field F is an infinite sequence {a_0,a_1,a_2,...} over F. Equivalently, it is a function ...

A group is called a free group if no relation exists between its group generators other than the relationship between an element and its inverse required as one of the ...

An equation of the form f(x,y,...)=0, where f contains a finite number of independent variables, known functions, and unknown functions which are to be solved for. Many ...

Consider h_+(d) proper equivalence classes of forms with discriminant d equal to the field discriminant, then they can be subdivided equally into 2^(r-1) genera of ...

Any symmetric polynomial (respectively, symmetric rational function) can be expressed as a polynomial (respectively, rational function) in the elementary symmetric ...

An irrational number x can be called GK-regular (defined here for the first time) if the distribution of its continued fraction coefficients is the Gauss-Kuzmin distribution. ...

A generalized eigenvector for an n×n matrix A is a vector v for which (A-lambdaI)^kv=0 for some positive integer k in Z^+. Here, I denotes the n×n identity matrix. The ...