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Algebraic structure: Quiz


Question 1: If q > 1 is a power of a prime number, then there exists (up to isomorphism) exactly one ________ with q elements, usually denoted Fq, or in the case that q is itself prime, by Z/qZ.
Field (mathematics)Finite fieldGroup (mathematics)Ring (mathematics)

Question 2: ________: a ringoid such that S is a monoid under each operation.
Ring (mathematics)SemiringGroup (mathematics)Algebraic structure

Question 3:
  • ________ (also Grassmann algebra): a graded algebra whose anticommutative outer product, denoted by infix ∧, is called the exterior product.
    Representation theoryClifford algebraExterior algebraVector space

Question 4: Structures whose axioms unavoidably include nonidentities are among the most important ones in mathematics, e.g., fields and ________.
Hilbert spaceVector spaceMatrix (mathematics)Group (mathematics)

Question 5: For example, neither the product of ________ nor a free field over any set exist.
Prime numberIntegral domainCommutative ringField (mathematics)

Question 6: M is at minimum an ________ under vector addition, with distinguished member 0.
Group (mathematics)Abelian groupGroup homomorphismSimple group

Question 7: ________, denoted by concatenation, is the vector multiplication.
Ring (mathematics)Matrix multiplicationMatrix (mathematics)Vector space

Question 8: ________: a group whose S has a compatible smooth manifold structure.
General linear groupLorentz groupLie groupGroup (mathematics)

Question 9: ________, Hilbert spaces, Inner product spaces
Metric spaceBanach spaceComplete metric spaceVector space

Question 10:
  • ________: an exterior algebra with a symmetric bilinear form Q: V×VK.
    Vector spaceSpinorClifford bundleClifford algebra


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