Seeing that Liu Maosheng had not spoken, Chen Zhou did not ask any more.

On the podium, Professor Atin was talking endlessly about the content of the Ring Theory.

Fractional ring theory is one of the important branches of ring theory, which refers to the theory of rings and modulus with fractional structures.

As for the study of fractional rings and fractional modes, it began as early as 1854.

At that time, Gloria introduces the group algebra K[G] on the domain K, which is the group G fractional K algebra.

Another early example of a subordinarial ring is a polynomial ring on the field of real numbers R.

Chen Zhou listened to Professor Ting's narration and couldn't help but think of the non-exchange ring.

Chen Zhou estimated that the reason why Professor Atin talked about the sub-ring theory was also because he was looking for a breakthrough point from the sub-ring theory.

The main driving force for the initial development of fractional loops and modes is the exchange of projective algebraic clusters in algebraic geometry, which forms one of the basic methods in the study of algebraic geometry.

However, the development of subordinative rings and modulos has entered a new era because of the impetus of noncommutative algebraic geometry and group representation theory.

The theory of group fractional rings is very active and fruitful.

It is also because of its close connection with many branches of mathematics that it has aroused the interest of a large number of mathematicians.

And as many people as they study, the development of this branch of mathematics will naturally be promoted.

This is also the reason why any branch of mathematics, or any field, can continue to develop.

"An example of fractional ring theory is the theory of arbitrary group division of non-commutative rings, which plays an important role in the theory of group action on rings and fixed points, group representation, and especially in the stable Clifford theory......"

Hearing Professor Ting's words, Chen Zhou's guess was even more firm.

The Fractional Ring Theory is definitely a breakthrough point that Professor Atin is looking for.

On the podium, Professor Atin began to explain the role of Clifford's theory and the role of the sequential ring theory.

Under the podium, Chen Zhou began to concentrate on two things, listening to Professor Ting's explanation, while pondering this thing by himself.

Chen Zhou understands the content of the sub-ring theory.

After all, Professor Atin gave him some of the information in this regard.

In addition to what Professor Artin just mentioned, the theory of the order of the non-commutative ring, and the resulting theory of the order of the group.

It is an important basic component of number theory, algebraic representation theory, noncommutative algebraic geometry, dimensionality theory, and ring theory.

In addition, the theory of fractional rings, though important.

However, what is more important is the fractional loop research method.

On stage, Professor Atin has extended to non-commutative rings.

Offstage, Chen Zhou not only followed the professor's train of thought, but also thought about the first attribute of the sequential ring theory.

This first property makes "A=⊕(n inN0)An=A0⊕A1⊕A2⊕......" a hierarchical ring.

Of course, this dual-purpose approach mainly follows Professor Artin's thinking.

The so-called thinking, Chen Zhou is only superficial, never deep.

As Professor Atin recounts, time flies.

Chen Zhou also listened very comfortably.

This kind of side-by-side quotation, completely detached from the PPT prepared in advance, sounds, is still more interesting.

Of course, this also tests the professor's ability even more.

But this is not a problem for Professor Atin at all.

Because, Chen Zhou has already found out.

Professor Artin's PPT, from the very beginning, was a "teleprompter".

This PPT is a total of 5 pages!

No more than 10 words on each page!

Basically, it's a keyword that gives you a hint of what you're talking about.

As for the specific content, it was all Professor Artin's unscripted speech that he carried out with his own ability.

"I finally know now. Liu Maosheng quietly tilted his head and said something to Chen Zhou.

Chen Zhou asked curiously, "What do you know?"

Liu Maosheng scolded Professor Atin on the podium with his mouth: "I finally know, why is your mentor so awesome!"

Zeng Zigu also came over and whispered: "The big guy is the big guy, I finally saw it today." ”

Chen Zhou smiled softly: "Should I humbly accept your praise on behalf of my mentor?"

Liu Maosheng immediately waved his hand, and said with a smile: "That's not necessary, if you have a chance, you take Professor Ating, and we will praise him in person." ”

Chen Zhou: "......"

Professor Atin on the podium turned the PPT to the last page.

This page is about the generalization of a theorem in G-fractional loops.

However, Professor Atin was not in a hurry to give his own lecture on the key words on this page.

Instead, he whispered a few words to the staff in the auditorium.

The staff understood what Professor Atin meant, and after leaving, Professor Atin began to return to the PPT.

"Here, we agree that G is a group, R is a binding ring with a unitary element, and further set R to be a G-fractional ring, that is, R=⊕(g∈G)Rg......"

Listening to Professor Ting's words, Chen Zhou was slightly stunned.

It turns out that this last page is not what Professor Atin himself wants to talk about.

It's for everyone by Professor Artin.

That is, Professor Atin assigned an exercise.

It is a proof of the generalization of a theorem about G-fractional loops.

On the stage, Professor Atin was still talking about the content of the "question stem".

Offstage, many students began to be dumbfounded.

Professor Artin, are you sure you're not mistaken?

Are you sure this is a proof to be generalized on the fly?

Are you sure this isn't a proof of SCI?

They felt that Professor Atin was embarrassed.

Other professors, with the exercises in class, still have a degree to some extent.

You came out directly with that research topic, and it turned out to be a paper.

Isn't that a bit too much?

Chen Zhou's idea is actually similar.

But more than that, I am still eager to try.

Chen Zhou felt that Professor Ting's question was just used to test his learning during this time.

The information obtained from Professor Artin, Chen Zhou did not slack off.

“...... So, we can get a corollary: let M∈Mod(R▕S), then right?? ∈Zi∈S and Zi = ⊕(g∈G)Zi,g{Re-modulus and }. ”

"If g∈Supp(Zi) and have Re-homeomorphism?? :Zi,g→M,then?? The only expansion into R-homomorphism?? e：Zi→M。 ”

"As for this inference......"

As he spoke, he looked at the time, then looked up at the crowd under the podium and said, "Just give everyone 10 minutes to think about it." ”

After Professor Atin finished speaking, he stepped off the podium and temporarily disappeared from everyone's field of vision.

And Artin's words instantly made the podium noisy.

"Good guy, worthy of being a master of mathematics, who are you looking down on in these 10 minutes?"

"Professor Artin, do you really think that in 10 minutes I can sort out what you just said?"

"Anyway, I can't figure it out, na, look at my notes, I haven't memorized all ......"

"I guess I can only look at the professors......