I came here because I was trying to learn about quaternions, and I wanted to make sure I understood some of the terms (like "ring") that were being used to describe it. I'm so glad you ended up using quaternions as an example! This'll probably save me an hour or so of mental grappling.
Varies by source. I think accepted practice is to state up front whether your definition uses it or not. In fact, rings without identity are often referred to in print as rngs. For undergraduate ring theory, it's better to keep the identity. The only hitch is that ideals become rngs - if I contains the identity, then I = R.
Without more, I'd think addition and multiplication, so the resulting object is a subring (which means we need to pay attention the multiplicative identity). We could also ask for the ideal generated by a set of elements, which includes products with all elements of the ring itself.
Most of the ring definitions i`ve seen don`t include the unit for multiplication and you did include it. Is there some kind of ambiguity in this definition or a most accepted one?
I came here because I was trying to learn about quaternions, and I wanted to make sure I understood some of the terms (like "ring") that were being used to describe it. I'm so glad you ended up using quaternions as an example! This'll probably save me an hour or so of mental grappling.
Varies by source. I think accepted practice is to state up front whether your definition uses it or not. In fact, rings without identity are often referred to in print as rngs. For undergraduate ring theory, it's better to keep the identity. The only hitch is that ideals become rngs - if I contains the identity, then I = R.
this is the best lecture on you tube
Generators in rings is the generator of that ring under addition?am i correct?
Without more, I'd think addition and multiplication, so the resulting object is a subring (which means we need to pay attention the multiplicative identity). We could also ask for the ideal generated by a set of elements, which includes products with all elements of the ring itself.
Most of the ring definitions i`ve seen don`t include the unit for multiplication and you did include it. Is there some kind of ambiguity in this definition or a most accepted one?
Bob can I please ask what camera you use for your videos? And do you have a mic? Thank you, keep up the good work!
That's the plan. Probably only a few videos a week if that. I'l' just add them to the Abstract Algebra playlist.
I bet he spend time at gym after recording this.
Excellent! Thank you.
i just noticed that Matrices constitute a ring! it is more nontrivial compared to the ring of rational numbers
Great stuff
9:21 ".. and so on." What are you going to lose by moving up further? You've already lost everything!
I'm told the sedonions are useful, which follow the octonions.
Captions would be nice. Thanks fo the video.
Nice!!!
Nice
Is this like where you would begin studying ring theory?
Yes.
thanks alot this really helped! :)
Thanks!
Wait til you learn about algebras!