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Direct product
Meaning
Noun
●
In Set theory:
The set
of all
possible
tuples
whose
elements
are
elements
of given,
separately
specified
, sets.
●
In Group theory:
Such a set of
tuples
formed
from two or more
groups
,
forming
another group whose group
operation
is the component-wise
application
of the
original
group
operation
s and of which the
original
groups
are
normal
subgroups.
●
Such a set of
tuples
formed
from two or more
rings
,
forming
another
ring
whose
operations
arise
from the component-wise
application
of the
corresponding
original
ring
operations
.
●
In Topology:
A
topological space
analogously
formed
from two or more (
up to
an
infinite
number of)
topological space
s.
●
In Mathematics:
Any of
a number of
mathematical
objects
analogously
derived
from a given
ordered set
of
objects
.
●
In Category theory:
A
high-level
generalization
of the
preceding
that
applies
to
objects
in an
arbitrary
category
and
produces
a new
object
constructable
by
morphisms
from each of the
original
objects
.
Sourced from
Wiktionary
Synonyms
Product
Categorical Product
Cartesian Product
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