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  2. Klein four-group - Wikipedia

    en.wikipedia.org/wiki/Klein_four-group

    V is the symmetry group of this cross: flipping it horizontally (a) or vertically (b) or both (ab) leaves it unchanged.A quarter-turn changes it. In two dimensions, the Klein four-group is the symmetry group of a rhombus and of rectangles that are not squares, the four elements being the identity, the vertical reflection, the horizontal reflection, and a 180° rotation.

  3. Extended Euclidean algorithm - Wikipedia

    en.wikipedia.org/wiki/Extended_Euclidean_algorithm

    For example, if the polynomial used to define the finite field GF(2 8) is p = x 8 + x 4 + x 3 + x + 1, and a = x 6 + x 4 + x + 1 is the element whose inverse is desired, then performing the algorithm results in the computation described in the following table.

  4. Separable extension - Wikipedia

    en.wikipedia.org/wiki/Separable_extension

    If E is an extension of F in which f is a product of linear factors then no square of these factors divides f in E[X] (that is f is square-free over E). [6] There exists an extension E of F such that f has deg(f) pairwise distinct roots in E. [6] The constant 1 is a polynomial greatest common divisor of f and f '. [7]

  5. Ext functor - Wikipedia

    en.wikipedia.org/wiki/Ext_functor

    An extension of A by B is called split if it is equivalent to the trivial extension. There is a one-to-one correspondence between equivalence classes of extensions of A by B and elements of Ext 1 R (A, B). [9] The trivial extension corresponds to the zero element of Ext 1 R (A, B).

  6. Simple extension - Wikipedia

    en.wikipedia.org/wiki/Simple_extension

    A field extension L/K is called a simple extension if there exists an element θ in L with L = K ( θ ) . {\displaystyle L=K(\theta ).} This means that every element of L can be expressed as a rational fraction in θ , with coefficients in K ; that is, it is produced from θ and elements of K by the field operations +, −, •, / .

  7. Chegg - Wikipedia

    en.wikipedia.org/wiki/Chegg

    Chegg began trading shares publicly on the New York Stock Exchange in November 2013. [15] Its IPO was reported to have raised $187.5 million, with an initial market capitalization of about $1.1 billion. [16] In 2014, Chegg entered a partnership with book distributor Ingram Content Group to distribute all of Chegg's physical textbook rentals ...

  8. Partially ordered set - Wikipedia

    en.wikipedia.org/wiki/Partially_ordered_set

    In our running example, {,,} and {} are the maximal and minimal elements. Removing these, there are 3 maximal elements and 3 minimal elements (see Fig. 5). Upper and lower bounds: For a subset A of P, an element x in P is an upper bound of A if a ≤ x, for each element a in A.

  9. Fundamental theorem of Galois theory - Wikipedia

    en.wikipedia.org/wiki/Fundamental_theorem_of...

    The field E H is a normal extension of F (or, equivalently, Galois extension, since any subextension of a separable extension is separable) if and only if H is a normal subgroup of Gal(E/F). In this case, the restriction of the elements of Gal(E/F) to E H induces an isomorphism between Gal(E H /F) and the quotient group Gal(E/F)/H.