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