Understanding Associativity of Multiplication Modulo n

  • Thread starter Thread starter sush4sep
  • Start date Start date
  • Tags Tags
    Multiplication
sush4sep
Messages
1
Reaction score
0
please explain me associativity for multiplication modulo n
 
Physics news on Phys.org
? Associativity for any binary operation is just (a*b)*c= a*(b*c). The point is that this allows us to extend the binary operation (defined for two operands) unambiguously to any number. I am not sure what you mean by "explain it for multiplication modulo n".

Perhaps this: let a, b c be numbers. Then (ab)c= a(bc) (mod n) if and only if (ab)c- a(bc) (mod n) which is the same as saying that (ab)c- a(bc), as an "ordinary" number, is a multiple of n. But in fact, because the usual multiplication of integers is associative, (ab)c= a(bc) so (ab)c- a(bc)= 0= 0(n) is a multiple of n.
 

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
View full post »

Similar threads

I Dfns group action & group, written in terms of the other
Replies
26
Views
377
B What is the identity element in the group {2,4,6,8} under multiplication mod 10?
Replies
9
Views
3K
I Multiplication in projective space
Replies
7
Views
2K
MHB 412.0.6 Find all integers n for which this statement is true, modulo n.
Replies
1
Views
1K
MHB Proof the set with the multiplication is a group
Replies
1
Views
1K
Definition of Finite Field: Addition and Multiplication Groups
Replies
1
Views
2K
I Trouble with a passage in Zariski & Samuel's Commutative algebra text
Replies
5
Views
625
I Name of distance to nearest multiple of n function?
Replies
1
Views
1K
A About universal enveloping algebra
Replies
19
Views
3K
A Structure of modulo-integer matrix group GL(r,Z(n))?
Replies
17
Views
6K

Hot Threads

Recent Insights

Back
Top