Endomorphism
المؤلف:
Lang, S.
المصدر:
Algebra, rev. 3rd ed. New York: Springer-Verlag, 2002.
الجزء والصفحة:
...
14-7-2020
1118
Endomorphism
The term endomorphism derives from the Greek adverb endon ("inside") and morphosis ("to form" or "to shape").
In algebra, an endomorphism of a group, module, ring, vector space, etc. is a homomorphism from one object to itself (with surjectivity not required).
In ergodic theory, let 
be a set, 
a sigma-algebra on 
and 
a probability measure. A map 
is called an endomorphism (or measure-preserving transformation) if
1. 
is surjective,
2. 
is measurable,
3. 
for all 
, where 
denotes the pre-image of 
.
An endomorphism is called ergodic if it is true that 
implies 
or 1, where ![T^(-1)A=<span style=]()
{x in X:T(x) in A}" src="https://mathworld.wolfram.com/images/equations/Endomorphism/Inline14.gif" style="height:17px; width:154px" />.
REFERENCES:
Lang, S. Algebra, rev. 3rd ed. New York: Springer-Verlag, 2002.
الاكثر قراءة في نظرية الاعداد
اخر الاخبار
اخبار العتبة العباسية المقدسة
