/sci/ - Science & Math

>>9609872
>modern algebra lecture
>professor asks class to define the characteristic of a ring
>classmate flips to the page in the book with the definition and paraphrases "It's the least positive integer n such that nx = 0 for all x in the ring."
>I chime in and say that nx is not necessarily the same thing as n · x, nx is multiplication while n · x is summing x with itself n times.
>professor says I'm being pedantic, multiplication is repeated addition. We move on.
>as I'm sitting through the rest of the lecture, I think of the ring [math]M_{2}(\mathbb{Z}_{2})[/math].
>you can sum the matrices in [math]M_{2}(\mathbb{Z}_{2})[/math], but you cannot multiply them by an integer.
>didn't ask professor about this case because too much of a pussy.
Am I being autistic and pedantic, or was the definition given by my classmate valid? I usually don't win when I disagree with professors, but I would like to make sure that lies are not being taught in class.

What shoould I study in uni if I want a job like steve irwin?