algebraic set


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algebraic set

[¦al·jə¦brā·ik ′set]
(mathematics)
A set made up of all zeros of some specified set of polynomials in n variables with coefficients in a specified field F, in a specified extension field of F.
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According to authors Vasantha Kandasamy and Smarandache, the Neutrosophic set is a nice composition of an algebraic set and indeterminate element of the real world problem.
The proof of Corollary 1 shows the existence of an algebraic set [S.
the graph of the mapping is contained in an irreducible complex n-dimensional algebraic set in [C.
4] is also a closed, real algebraic set of dimension at most 2n - 3.
1) -i) Since W is an irreducible algebraic set in D of dimension n - 1, there exists an irreducible polynomial h in [C.
The set f(W) is an irreducible algebraic set of dimension n - 1 in D', then there exists an irreducible polynomial [?
t]) for L moving in a non-trivial family over some algebraic set [DELTA].
The other six contributions examine the relationship between nonnegativity and sums of squares, compare the different notions of duality, find spectrahedral approximations of convex hulls of algebraic sets, extend algebraic certificates of real algebraic geometry to noncommutative polynomials, and derive sums of Hermitian squares.
Appendices cover such background material as the Tarksi-Seidenberg theorem and algebraic sets.
Based on a June 2005 summer school, this series of 24 lectures introduces the algebraic sets, sheaf theory, and homological algebra leading to the definition and alternative characterizations of local cohomology.