Well, Following you since Very long time for problem solving, After long time, Today I needed To recall some concepts of Ring theory and I found you Again.... Made me smile... Thank you Professor... 🙌🏻😀
Great video, i've noticed you define a ring without the need for a neutral element for the second operation, but all textbooks I've seen insist on needing the neutral element for it to be called a true ring. I guess that's a matter of convention ?
You're right, it's a matter of convention. Here doi:10.1080/0025570X.2018.1538714 is a good defence of all rings have multiplicative identity: it allows us to define products of any finite (even length 0) sequence of elements.
In Wikipedia, it is stated that a "ring" does have a multiplicative identity, meaning that (R, *) forms a monoid rather than just a semigroup. Additionally, "rng" satisfies the conditions mentioned in your video.
No, in the orginal German it referred to a group of related objects, much like groups. Think of how a phrase like "drug ring" is used in English nowadays.
I teach my class from Judson (abstract.ups.edu/), but use some other books as self references: essentially anything that is nearby, which recently has been Dummit and Foote
I found a discussion of this question: math.stackexchange.com/questions/61497/why-are-rings-called-rings I have to admit, I wasn't aware of any of this before reading through this page.
The operations both work like the operations for Z, but 1 isn't in 2Z, so there can't be an identity. (There's always an additive identity in a ring by definition, so when he says there isn't an identity, he means that there isn't a multiplicative identity.)
There is no element by which to multiply another element so that it would remain the same. This element in R is 1, but in 2R it's missing because 2R contains only even numbers.
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This is such a great channel. A gem.
Great work by Michael Penn. Amazing
This series is GOLD It is so much better than my professor. Thanks a lot
I'm just gonna leave a comment below in order to promote this channel
Well, Following you since Very long time for problem solving,
After long time,
Today I needed To recall some concepts of Ring theory and I found you Again.... Made me smile...
Thank you Professor... 🙌🏻😀
This video felt like 10 seconds lol. I really wish you did a full series on abstract algebra with this phenomenal level of clarity.
Great video, i've noticed you define a ring without the need for a neutral element for the second operation, but all textbooks I've seen insist on needing the neutral element for it to be called a true ring. I guess that's a matter of convention ?
You're right, it's a matter of convention. Here doi:10.1080/0025570X.2018.1538714 is a good defence of all rings have multiplicative identity: it allows us to define products of any finite (even length 0) sequence of elements.
In Wikipedia, it is stated that a "ring" does have a multiplicative identity, meaning that (R, *) forms a monoid rather than just a semigroup. Additionally, "rng" satisfies the conditions mentioned in your video.
But why is it called a ring? Does it have to do with how you can imagine the structure conceptually?
No, in the orginal German it referred to a group of related objects, much like groups. Think of how a phrase like "drug ring" is used in English nowadays.
@@SP-qi8ur awesome thanks. Any sources you’d recommmend?
Good introduction to Ring Theory
amazing explanation
Hey great video. Thanks for sharing! Btw which book do you follow for Abstract Algebra?
I teach my class from Judson (abstract.ups.edu/), but use some other books as self references: essentially anything that is nearby, which recently has been Dummit and Foote
Why is it called a ring?
I found a discussion of this question: math.stackexchange.com/questions/61497/why-are-rings-called-rings
I have to admit, I wasn't aware of any of this before reading through this page.
@@MichaelPennMath Thanks!
What is the title of the next video?
Are you related to the Penn acting family?
I dont understand why does not 2Z have any identity element?
The operations both work like the operations for Z, but 1 isn't in 2Z, so there can't be an identity. (There's always an additive identity in a ring by definition, so when he says there isn't an identity, he means that there isn't a multiplicative identity.)
@@iabervon so that means 2Z is a ring since it has additive identity!
There is no element by which to multiply another element so that it would remain the same. This element in R is 1, but in 2R it's missing because 2R contains only even numbers.
hi
Are you sure you haven't forgotten closure under multiplication in your definition?
It's implicit in referring to + and . as binary operations.
What's the use of this?
gud vidya
clutch
Totally didn't see this lol
I think I have a crush on you 😳
the nomenclature is just plain dumb...a ring?
Is this Barney Stinson trying to hit on a woman by telling he is a mathematician ?