User:Richard Pinch/sandbox-14

Generating set

Generating set may refer to

• For an algebraic object $A$, a set $S$ such that the smallest subobject of $A$ containing $S$ is $A$ itself: a set $S$ such that $A$ consists of all elements resulting from applying the algebraic operations of $A$ to combinations of elements of $S$.
  • A spanning set for a module over a ring, or a vector space;
  • The set of generators in a group presentation.
• For the special cases of a free algebraic system on a given set of generators:
  • Free algebra:
  • Free group;
  • Free semi-group.

See also Generator of a category.

Identity (disambiguation)

Identity may refer to

• An algebraic identity, an equality that holds true for all values of the variables involved within some domain of validity, or Quasi-identity
  • Bianchi identity
  • Buchstab identity
  • Hermite identity
  • Ricci identity
  • Spitzer identity
  • Vaughan identity
  • Wald identity
  • Waring identity
• An property valid for all elements of a certain algebraic structure
  • Alternative identity
  • Capelli identity
  • Polarisation identity
• A transformation which sends an element to itself
  • Identity map
• An element of an algebraic structure which is a neutral element for an algebraic operation
  • Identity element
    • Identity problem
  • Identity matrix
  • Ring with identity

Order (disambiguation)

The term "order" has far too many meanings for an article under that title to fix on a single one. There are at least three main groups of meanings:

• Cardinality of a finite algebraic system
  • Order of a group, Lagrange theorem
  • Order of a field, finite field
• Numerical invariant of an algebraic or analytic system
  • Approximation order
  • Average order of an arithmetic function, Normal order of an arithmetic function
• A certain binary relation
  • Order on a set, Partial order, Order relation
    • Directed order
    • Discrete order
    • Hopf order = Larson order, Greither order
    • Interval order
    • Lexicographic order
    • Pointwise order
    • Total order, Totally ordered set = Linear order
    • Trivial order
  • Related concepts
    • Pre-order = quasi-order, pre-ordering, quasi-ordering, weak order, preference
  • Derived concepts
    • Order statistic
    • Order topology
    • Order type

Trace (disambiguation)

Trace may refer to

• Trace on a field extension
• Trace of a square matrix
• Trace on a C*-algebra
  • Character of a C*-algebra
• Trace of a trace-class operator
• An element of a trace monoid
• Reduced trace on a central simple algebra
• Dixmier trace
  • Wodzicki residue = Non-commutative residue