Question

so what we learned today ....

if a doesnt divide b, but a divides bc; then a divides c.

Answer 1

we also learned that if a divides bc, then a divides bcn ..... 30 minutes of my life gone :/

Answer 2

Believe it or not, that's not inherently obvious. Depending on what structures you're using, if a doesn't divide b, but a does divide bc, it doesn't necessarily divide c.

Answer 3

number theory ... :)

Answer 4

I'ma delete this shortly afterward, but can anyone help me
http://openstudy.com/study#/updates/5064b1f2e4b0583d5cd3facc
Also, does that apply for matrix algebra?

Answer 5

mattrix algebra has quirks in that its .. cant recall. ring, field, group ??

Answer 6

Number theory is an easy example, but you can define a ring with zero divisors, and suddenly, if ab=0, then neither a nor b must be 0.

Answer 7

o.o show me the logic!

Answer 8

teacher did show us at the begining of the year about her thesis work on abstract algebra and made us write up Zmod 12 tables for addition and multiplication

Answer 9

Zmod12 is a nice example. 2*6=0=3*4

Answer 10

No that's not helpful I don't understand zmods lool

Answer 11

2*6 mod 12=0
If you understand modular multiplication, it's what you would imagine Zmod12 would be.

Answer 12

if a not| b; the (a,b)=1; therefore 1 = ax+by

multiply each side by c

c = acx+bcy

a|acx

a|bcy , it was given in the thrm that a|bc

therefore

a | (acx+bcy)
a | c

Answer 13

all the 0 mod 12s have no recipricals :)

Answer 14

.... er, no multiplicative inversai

Answer 15

I look at wikipedia and see funny symbols.
http://en.wikipedia.org/wiki/Modular_arithmetic
I quit this party.

Answer 16

There must be some way out of here, said the joker to the thief.

There's too much confusion ... I can't get no relief

Answer 17

Well, if it's coprime to 12 it has a multiplicative inverse....