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A polynomial p(x)=sumc_ix^i is said to split over a field K if p(x)=aproduct_(i)(x-alpha_i) where a and alpha_i are in K. Then the polynomial is said to split into linear ...

A stack F on a topological space X is said to be a stack of groupoids if for each open subset U subset= X, the category F(U) is a groupoid.

sum_(k=-infty)^infty(a; m-k)(b; n-k)(a+b+k; k)=(a+n; m)(b+m; n).

The locus of points whose first polars with regard to the curves of a linear net have a common point. It is also the locus of points of concurrence of line polars of points ...

Let P be a prime ideal in D_m not containing m. Then (Phi(P))=P^(sumtsigma_t^(-1)), where the sum is over all 1<=t<m which are relatively prime to m. Here D_m is the ring of ...

A theorem which specifies the structure of the generic unitary representation of the Weyl relations and thus establishes the equivalence of Heisenberg's matrix mechanics and ...

Let P(L) be the set of all prime ideals of L, and define r(a)={P|a not in P}. Then the Stone space of L is the topological space defined on P(L) by postulating that the sets ...

Let (K,|·|) be a complete non-Archimedean valuated field, with valuation ring R, and let f(X) be a power series with coefficients in R. Suppose at least one of the ...

The strongly embedded theorem identifies all simple groups with a strongly 2-embedded subgroup. In particular, it asserts that no simple group has a strongly 2-embedded ...

Given three curves phi_1, phi_2, phi_3 with the common group of ordinary points G (which may be empty), let their remaining groups of intersections g_(23), g_(31), and g_(12) ...