A perhaps better way to understand an ideal is that it is analogous to that of a normal subgroup in group theory, Normal subgroups were those that had the extra structure/conditions necessary in order for us be able to construct a quotient group from them, in this case ideals are those subrings with the necessary conditions for us to be able to construct a quotient ring out of them, these extra conditions being for all r in the ring and i in the sub ring ir and ri are necessarily elements of our sub ring. In other words Ideals are the class of rings we are allowed to construct a quotient ring out of, there is in fact a theorem stating so: Theorem: If I subset of R is an ideal, then R/I is a ring
I went from hating algebra to loving it because of your videos...thank you so much!
you make these annoying concepts so clear! Thanks a lot!
Studying for my final and this was so helpful. Thank you!
beautifully explained
Sir, plz show to how to find subring , ideal .max. ideal ,prime ideal of any given ring.. ..
Why does it have to be an ideal and not just a sub Ring?
A perhaps better way to understand an ideal is that it is analogous to that of a normal subgroup in group theory, Normal subgroups were those that had the extra structure/conditions necessary in order for us be able to construct a quotient group from them, in this case ideals are those subrings with the necessary conditions for us to be able to construct a quotient ring out of them, these extra conditions being for all r in the ring and i in the sub ring ir and ri are necessarily elements of our sub ring. In other words Ideals are the class of rings we are allowed to construct a quotient ring out of, there is in fact a theorem stating so:
Theorem: If I subset of R is an ideal, then R/I is a ring
@@datsmydab-minecraft-and-mo5666 I came back to this video and just noticed that I completely misunderstood the question. Thanks for answering it!
cuz it has to be the kernel of a homomorphism
Week
"Weak"
your "inglis is week" I guess
Not goood