# User:Richard Pinch/sandbox-14

From Encyclopedia of Mathematics

## Contents

# 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:

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
- An property valid for all elements of a certain algebraic structure
- A transformation which sends an element to itself
- An element of an algebraic structure which is a neutral element for an algebraic operation

# 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
- 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 on a set, Partial order, Order relation

# Trace (disambiguation)

**Trace** may refer to

- Trace on a field extension
- Trace of a square matrix
- Trace on 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

**How to Cite This Entry:**

Richard Pinch/sandbox-14.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Richard_Pinch/sandbox-14&oldid=51679