Recent content by karthikvs88

There was never, a party, it was just me (and later you). Anyway, check out Dummit & Foote, it is a better and updated reference for algebra.

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Homework Statement Problem 3.5.2 Let R be a ring such that the only right ideals of R are (0) and R. Prove that either R is a division ring or that R is ring with a prime number of elements in which ab = 0 for every a, b \in R. Homework Equations The Attempt at a Solution...

Let R be a ring in which x3=x for every x in R. Prove that R is a commutative ring. This is (word-for-word) in Herstein, Topics in Algebra, Ch. 3 sec. 4, problem 19. Apparently, Herstein commented that this one problem generated more mail than the entire remainder of the book. The proof...

Hi, I figured it out, yeah I guess we can always find p and q such that pn - qm equals any value. Since we can find i and j such that im + jn = 1 (a-b)im + (a-b)jn = (a-b) hence our p and q would be (a-b)j and -(a-b)m. Still don't know how Pigeon hole principle is used here though.

Hey mathmadx, I am not aware of this result you have used, "Well, as gcd(n,m)=1, we can ALWAYS find p and q such that pn-qm equals any value, in particular a-b. " What I do know is, "If a and b are integers, not both 0, then gcd(a,b) exists; and we can find integers m and n such that...

Homework Statement Using pigeon hole principle, prove that if m and n are relative prime integers and a and b are any integers, there exists an integer x such that x = a mod m, and x = b mod n.Homework Equations noneThe Attempt at a Solution data: m|(x -a) and n|(x-b) hence we can write...