Module action sends zero to zero?

In summary, "Module action sends zero to zero" is a phrase commonly used in mathematics and computer science to describe a function or operation that takes in a value of zero and returns a result of zero. It is often used in scientific research to analyze and understand mathematical models or computer programs, and can be seen in action in functions such as calculating the area of a rectangle with a length or width of zero. Its significance lies in its unique behavior when given an input of zero, but there can be exceptions depending on the context and application.
  • #1
geor
35
0
Hello,

Excuse me if I ask something obvious here, but I can't
prove it..

Say R is a ring and M an R-module.
So, 0 \in M as M is an abelian group.

I guess r0=0, no?!

Can you tell me how we prove that?

Again, sorry if I ask something obvious..
 
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  • #2
It's true:

r0 = r(0 + 0) = r0 + r0. Canceling r0 from both sides gives 0 = r0.
 
  • #3
adriank said:
It's true:

r0 = r(0 + 0) = r0 + r0. Canceling r0 from both sides gives 0 = r0.

Oh, yes.. :shy:

Thanks a lot!
 

Related to Module action sends zero to zero?

1. What does "module action sends zero to zero" mean?

"Module action sends zero to zero" is a phrase commonly used in the field of mathematics and computer science. It refers to a function or operation that takes in a value of zero and returns a result of zero. This means that the function has no effect or does nothing when given an input of zero.

2. How is "module action sends zero to zero" used in scientific research?

In scientific research, the phrase "module action sends zero to zero" is used to describe a specific type of function or operation. It can be used to analyze and understand the behavior of mathematical models or computer programs, particularly when dealing with inputs of zero.

3. Can you give an example of "module action sends zero to zero" in action?

An example of "module action sends zero to zero" would be a function that calculates the area of a rectangle. If the length or width of the rectangle is zero, the function would return an area of zero, as a rectangle with no length or width has no area.

4. What is the significance of "module action sends zero to zero" in scientific calculations?

The phrase "module action sends zero to zero" is significant in scientific calculations because it represents a specific type of function that has a unique behavior when given an input of zero. This can be useful in simplifying and understanding complex mathematical or computational problems.

5. Are there any exceptions to "module action sends zero to zero"?

Yes, there can be exceptions to "module action sends zero to zero" depending on the context and application. For example, a function may return a result of zero even when given an input other than zero if specific conditions are met. It is important to consider the specific function and its intended use in order to determine any exceptions to this phrase.

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