Help me identify thyis maths symbol please

[mahaju]

This is an excerpt from an article I am reading. In the 2nd line the Z refers to set of integers I think, but what does Z/m mean? Does it mean the set {0,1, ..., m-1} (ie, the set of integers mod m) or does it mean something else?
Please help me out here.
Thanks in advance.

 

[andre_luis]

I may be wrong; But seems have some inconsistence on definition at 1/2 lines and postulation at 5/6 lines.

+++

 

[lostinxlation]

Well, the title says modular arithmetic. So, isn't it a division in modular arithmetic?

 

[FvM]

Does it mean the set {0,1, ..., m-1} (ie, the set of integers mod m) or does it mean something else?

Yes, Z/m is a set, but not a set of simple integers. It's members are sets of integers congruent modulo m.
Modular arithmetic - Wikipedia, the free encyclopedia

 

[mahaju]

Thank you very much
Considering the symbol to mean the set Z mod m the other parts of the article make a little more sense, but I still have many problems with this. For instance, do you have any idea what it means in line 5, that
Steps 1 and 3 are "no-ops" if Z/m is represented as {0,1,...,m-1}
What is "no-ops" and why the "if"? ( since Z/m means {0,1,...,m-1} )

Again, in this next section, R[x] means the set of all polynomials in R with variable x, that is, the coefficients of the variables in the polynomials are members of the ring R. So does that mean R[y][x] (line 2) is the set of polynomials of two variables x and y? And what is the difference between writing R[y][x] and R[x][y], because in later sections the articles hints that they are not the same, however it's not clear how they are different. Also, by analogy, R[y][x]/(x^n-y) would mean a set of polynomials that we get as remainder when we divide the members of the set in the numerator by the denominator. Is this right? Do I have to visualize this new set as something being finite like Z/m, or is it possible for this new set to have infinite members?

Thanks
:-D

 

[FvM]

There's pretty much literature about modular arithmethic and it's applications, e.g. in cryptography. So if the quoted literature isn't well understandable, look out for a different one. Once you have fully understood the properties of Z/m, the author's intentions will be hopefully more clear.

I'm not truely engaged with this stuff and don't feel qualified to teach it. I'm mostly happy to understand, what the mathematicians are talking about