What does module homomorphism mean?
Definitions for module homomorphism
mod·ule ho·mo·mor·phism
This dictionary definitions page includes all the possible meanings, example usage and translations of the word module homomorphism.
Wikipedia
Module homomorphism
In algebra, a module homomorphism is a function between modules that preserves the module structures. Explicitly, if M and N are left modules over a ring R, then a function f : M → N {\displaystyle f:M\to N} is called an R-module homomorphism or an R-linear map if for any x, y in M and r in R, f ( x + y ) = f ( x ) + f ( y ) , {\displaystyle f(x+y)=f(x)+f(y),} f ( r x ) = r f ( x ) . {\displaystyle f(rx)=rf(x).} In other words, f is a group homomorphism (for the underlying additive groups) that commutes with scalar multiplication. If M, N are right R-modules, then the second condition is replaced with f ( x r ) = f ( x ) r . {\displaystyle f(xr)=f(x)r.} The preimage of the zero element under f is called the kernel of f. The set of all module homomorphisms from M to N is denoted by Hom R ( M , N ) {\displaystyle \operatorname {Hom} _{R}(M,N)} . It is an abelian group (under pointwise addition) but is not necessarily a module unless R is commutative. The composition of module homomorphisms is again a module homomorphism, and the identity map on a module is a module homomorphism. Thus, all the (say left) modules together with all the module homomorphisms between them form the category of modules.
Numerology
Chaldean Numerology
The numerical value of module homomorphism in Chaldean Numerology is: 5
Pythagorean Numerology
The numerical value of module homomorphism in Pythagorean Numerology is: 7
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"module homomorphism." Definitions.net. STANDS4 LLC, 2024. Web. 28 Apr. 2024. <https://www.definitions.net/definition/module+homomorphism>.
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