Tags » Zero Divisors

A Rant on Definitions for Zero Divisors

Hmmm, well rant is probably over exaggerating, this is more like a heads up about definitions concerning zero divisors in a ring. In this post I will present different definitions of zero divisors in a… 432 more words

Commutative Rings

Introduction to Ring Theory (1)

Recall that in groups, one has only a binary operation *. Rings are algebraic structures with addition and multiplication operations – and consistency is ensured by the distributive property. 1,394 more words


Theorem 39: Euler's criterion

I’ve previously written about Fermat’s Little Theorem, which tells us that if is a prime and is not divisible by , then .  That’s not terribly exciting when , so let’s concentrate on odd primes in this post.  672 more words

Cambridge Maths Tripos

Luis R. Guzman, Jr. reblogged this on Guzman's Mathematics Weblog and commented:


Mathematical primer, part 4

After yesterday’s diversion on algebraic structures, we’re almost ready to move onto division. Subtraction is easy to derive from the natural numbers: if m < n in ℕ then there is a natural number k such that n = k + m, so we can write k = n – m. 1,098 more words


Proof of the Day (POD): Rings, Cancellation, and Zero Divisors

I’m going to try and start a new feature here, the “proof of the Day”.  It’s based on the crossfit idea of the Workout of the Day where they post a new workout everyday.  202 more words


Localization 1

I’m calling this “Localization 1″ since it is technically the beginning of the construction that we eventually want. But for now, I don’t even want to define what it means for a ring to be local, or why this may or may not be a (the) “localization.” 579 more words