May I ask how long you have been doing abstract math to get the kind of intuition that you have? Im doing Algebra as a last semester undergraduate course. I can not tell you enough how much you videos are helping me!
It depends on how you define ring and subring. If you don't require that a ring have a multiplicative identity, then yes, an ideal is a subring! However, if you require that all rings have a multiplicative identity (this is a more modern definition of a ring), then you also require that a subring must have the same multiplicative identity as the ring itself. Under this definition, ideals (with the exception of the unit ideal) are definitely _not_ subrings!
I was thinking the same, in fact, *every* *ideal* *is* *a* *subring.* A ring does not necessarily contain the multiplicative identity, if it does then we call the ring to be a *ring* *with* *identity.*
That was superrrrr superrrrr awesome explained with patience and details 😍😍😍 more power to youu brooo I've watched the three consecutive videos so far
Thank you!
May I ask how long you have been doing abstract math to get the kind of intuition that you have? Im doing Algebra as a last semester undergraduate course. I can not tell you enough how much you videos are helping me!
I think an ideal is a subring but remember a ring doesn't have to have a multiplicative identity
It depends on how you define ring and subring. If you don't require that a ring have a multiplicative identity, then yes, an ideal is a subring!
However, if you require that all rings have a multiplicative identity (this is a more modern definition of a ring), then you also require that a subring must have the same multiplicative identity as the ring itself. Under this definition, ideals (with the exception of the unit ideal) are definitely _not_ subrings!
I was thinking the same, in fact, *every* *ideal* *is* *a* *subring.* A ring does not necessarily contain the multiplicative identity, if it does then we call the ring to be a *ring* *with* *identity.*
i am attendin maths asters addis abeba university Ethiopia but i got you a week befor seriosly my algebra 1 541 course result was not good