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CH-quasigroup
In mathematics, a CH-quasigroup, introduced by , is a symmetric quasigroup in which any three elements generate an abelian quasigroup. "CH" stands for cubic hypersurface. References *{{Citation , last1=Manin , first1=Yuri Ivanovich , author1-link=Yuri Ivanovich Manin , title=Cubic forms , origyear=1972 , url=https://books.google.com/books?id=W03vAAAAMAAJ , publisher=North-Holland , location=Amsterdam , edition=2nd , series=North-Holland Mathematical Library , isbn=978-0-444-87823-6 , mr=833513 , year=1986 , volume=4 Non-associative algebra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasigroup
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups mainly in that they need not be associative and need not have an identity element. A quasigroup with an identity element is called a loop. Definitions There are at least two structurally equivalent formal definitions of quasigroup. One defines a quasigroup as a set with one binary operation, and the other, from universal algebra, defines a quasigroup as having three primitive operations. The homomorphic image of a quasigroup defined with a single binary operation, however, need not be a quasigroup. We begin with the first definition. Algebra A quasigroup is a non-empty set ''Q'' with a binary operation ∗ (that is, a magma, indicating that a quasigroup has to satisfy closure property), obeying the Latin square property. This states that, for each ''a'' and ''b'' in ''Q'', there exist uniqu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Hypersurface
In mathematics, a cubic form is a homogeneous polynomial of degree 3, and a cubic hypersurface is the zero set of a cubic form. In the case of a cubic form in three variables, the zero set is a cubic plane curve. In , Boris Delone and Dmitry Faddeev showed that binary cubic forms with integer coefficients can be used to parametrize order (ring theory), orders in cubic fields. Their work was generalized in to include all cubic rings (a is a ring (mathematics), ring that is isomorphic to Z3 as a Module (mathematics), Z-module),In fact, Pierre Deligne pointed out that the correspondence works over an arbitrary Scheme (mathematics), scheme. giving a discriminant-preserving bijection between Orbit (group theory), orbits of a GL(2, Z)-Group action (mathematics), action on the space of integral binary cubic forms and cubic rings up to isomorphism. The classification of real cubic forms a x^3 + 3 b x^2 y + 3 c x y^2 + d y^3 is linked to the classification of umbilical points of surf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
