Question

Meaning of property of modules

Meaning of property of modules

Answer 1

Answer:

I'm creating a module that needs a property of its own. I know I can manually define a property through the server manager, but I would like to create the property automatically from the module.

Is this answer is right

Answer 2

A module is a mathematical object in which things can be added together commutatively by multiplying coefficients and in which most of the rules of manipulating vectors hold. A module is abstractly very similar to a vector space, although in modules, coefficients are taken in rings that are much more general algebraic objects than the fields used in vector spaces. A module taking its coefficients in a ring R is called a module over R, or a R-module.

Modules are the basic tool of homological algebra. Examples of modules include the set of integers Z, the cubic lattice in d dimensions Z^d, and the group ring of a group.

Z is a module over itself. It is closed under addition and subtraction (although it is sufficient to require closure under subtraction). Numbers of the form nalpha for n in Z and alpha a fixed integer form a submodule since, for all (n,m) in Z,

nalpha+/-malpha=(n+/-m)alpha

and (n+/-m) is still in Z.

Given two integers a and b, the smallest module containing a and b is the module for their greatest common divisor, alpha=GCD(a,b).