An integral domain has sub domains. All together you get ten. We know there is an close connection between groups and manifolds. Can you have a kind of Mayer-Vietoris sequence between domains?
What I mean is let's say you have a map from an integral domain to a commutative ring, and another map to another commutative ring. And then you have a map from either commutative ring into a larger group.  So now can you put an "H" (homology groups) in front of each map? and if so would this work for all the sub-rings underneath the integral domain?

For example could you do the same with a Noetherian Ring and another Noetherian Ring. And you have an intersection between them. And you map into some larger ring. Can you apply the Mayer Vietoris  theorem? Or would there be an obstruction?




Apparently someone has already dealt with this question at this link


I put this on the internet because I do not want to ask a math or physics professor this question unless I think about it some more.

How to learn Musar [ethics]

How to learn Musar [ethics]? You would think this would be simple after all the effort put into the idea by Reb Israel Salanter.
 Some people emphasized one particular area of value. A good example is the Hafez Haim.
[Not to slander.]


What to me makes sense is in fact to take the Musar books of the rishonim [medieval writers] and plow through them. But to get a wider perspective what  I think is the best thing is to have one session of going through all the works of classical Musar [about 30 books] and another session of going through the writings of the disciples of Reb Israel Salanter. Plus one more session in classical Jewish world view issues like the Guide for the Perplexed of the Rambam and the Faiths and Doctrines by Saadia Gaon  . What happens is that this last step is omitted by most people and the result is people end up with view totally contrary to Torah,-- but think their views are from the Torah.

To learn Musar in yeshivas at all was subject to debate. But what I am suggesting is  a further step to add השקפה. World view issues. I see this as very important because I see that without this later step people really get ideas very much opposed to the Torah but think their ideas are OK because they heard them from some delusional maniac in the name of the Torah.

I have not given this much thought but I can say based on what I have seen that Musar [learning ethics is important, but without world view it can be highly distorted.]

The Hafetz Haim's books about not to slander and general Musar are in fact a great starting place to begin with.
[I should add that not to slander does not mean you can not warn your children about bad cults. That is even if there is one or two decent people in that cult you can still say the cult is bad. The reason is there is such a thing as group behavior, a social meme. Not only that but if the social meme itself is evil, then the group itself is evil.
_______________________________________________________________________


Appendix: For the general public: Musar means mainly medieval books of ethics. But also refers to books by the disciples of Israel Salanter.


Most Musar books do not go into world view issues except the Obligations of the Heart who makes in he first part of his Musar book. However Rav Moshe Haim Luzato did go into world view issues in detail but not in his Mesilat Yesharim.

Music for the glory of God

r18 A minor r3  p120 n1 r21

I have had a fascination with Halacha [Jewish Law] for a long time. I know that in one previous essay I must have sounded like I was knocking it. But I really meant to knock the misuse of the concept of Halacha and the pretense of people that pretend to know and keep it.

But now I wanted to deal with this subject in the correct way.  And this is not hard to present. In fact my very first year in yeshiva I was shown right away the correct approach towards halacah.
[Yeshiva has in general four years. The first year is for beginners.]  The yeshiva [Shar Yashuv] was doing Chulin which deals with ritual slaughter and things like that. It was perfect to show how to learn Halacha. For every law was more or less a self contained unit. So we would learn the law in the Talmud itself--the source of the law. Then we would trace it down through the Tur, Beit Joseph (by Joseph Karo) and Shulchan Aruch. (The Shulchan Aruch was also written by Joseph Karo and meant to be  a short version of the Beit Joseph so people could do fast review.)



 But that is really just to provide an introduction to the subject. To get a general idea that takes in the big picture what I recommend is this: To get Reb Chaim Soloveitchik's book, Chidushai HaRambam, and the books of his two disciples, Baruch Ber and Shimon Shkop. But even more important I would run out immediately and buy the Avi Ezri of Rav Shach.
If you have just one Tractate at home and just one of the above mentioned books, now you are prepared to learn Halachah.

What to do is to take one essay from and of the above mentioned books and learn it with the subject matter in the Gemara. Do not worry of you do not understand it at first. Just keep going over the same essay every day until it sinks in.

This small blog entry is not supposed to be exhaustive. It is rather just an introduction. I should go into the fact of the Maharaha, and Maharshal, and the Gra and the Beit Joseph that all shouted  and yelled about people that decide halachah from short versions of Halacha without knowing the actual Gemara.

Then to actually decide any particular Halacha what I do is to get to know the relevant sources. The first step is to know the subject in the Gemara itself with Tosphot. Then you need to see the Geonim. Often their opinions were not known, so this takes some digging. Then the Rishonim, Rambam, Rif Tur, Shulchan Aruch. After that there is usually no issue that does not become clear.

But if you need an immediate idea, then the best bet is to go directly to the Tur Beit Joseph.

If only more people would learn Halacah properly, a lot of issues would be resolved. Knowing what idolatry is or how to act in many situations would be clear.

Music for the glory of the God of Israel

r17 F major q3 q1 q5 q6 q7 r3 q96 e flat major

Learning fast. Say the words in order and go on is the way to learn Torah, Physics and Math.

Learning fast was an idea that for me had a lot of support. There were the popular speed reading books around in those days. Then there was a collage I applied to that was all about reading fast and going through a few book every week. Then Reb Simcha Wassermann gave me the Musar book אורחות צדיקים Ways of the Righteous that had a whole chapter about going through Shas lots of times fast. Even in violin I saw that when I prepared by just going through the piece straight lots of times I did a lot better at my violin lesson, than if I spend time on the single parts that were giving me trouble.

So in terms of Torah learning this is what I tried to do. At some point however it seemed to me that by just concentrating on a single Tosphot that I would make more progress than if I just read on. So my feeling is that for every subject one does he or she should combine both methods fast and in depth.

In fact,- because not everyone has a authentic Lithuanian yeshiva nearby, and it is wise to avoid hasidic cults so one does not lose his sanity, I think the best idea for Torah study is to buy one tractate and a book of Musar  and just learn them at home.

[Simcha Wassermann was incidentally the son of Reb Elchanan Wassermann the major disciple of the Chafetz Chaim. He was the one to recommend to me to go to the Shar Yeshuv yeshiva in NY which eventually got me to the Mir. I used to hang out with him and in his yeshiva in those ancient days. I ate with him and his wife on Shabat and went to his yeshiva at the end of classes in high school. But I can see today that to have gotten anywhere in Gemara I really needed to go to NY.]

In yeshiva it was possible for me to have long sessions. The normal yeshiva session was from about 915 until 205 and then Mincha. [5 hours]. The from 330 until 815 and then Maariv.  [Also circa 5 hours]. But since I left yeshiva I have found short sessions to be more workable for me.] That is if find I can not do that long stretch, then I try to break up the day into small segments. --Almost teh same way they do in high school.

In any case what I suggest is one session to go through the entire oral and written law words for word from beginning to end. That is Gemara Rashi Tosphot Mahrasha and Maharam  about a half a page per day. [That is about 40 minutes per day.] Then when you have gone through the Bavli that way then the Jerusalem Talmud in the same way-with the Pnei Moshe. Then the Tosephta, Mechilta Sifra Sifri and Midrashim.

[This would work well for Physics also I assume. The trouble is that Physics needs a lot of time just like Torah does. It is hard enough to get to any degree of expertise in one area.]

(White Anglo Saxon Protestant).

I grew up in a totally Wasp area. (White Anglo Saxon Protestant). There was only one other Jewish family within the city. For there was something wholesome and precious about the environment.


The story was that most of the property was owned by a Wasp corporation and we needed special, permission in order to buy a home there.



But ever since then I have never been sympathetic towards people that saw Wasps in a bad light. And I did notice a good deal of left wing politics was directly towards destroying communities like the one I grew up in and I have not thought that there was much merit in such an approach.

[In order for me to go to Hebrew school my mother had to drive me to a city that was far away every week.]

After some years we had to move so my Dad could be closer to his place of work at TRW when they had been contracted by NASA to built satellite communication by lasers and that was right up my Dad's area of expertise. So he was put in charge of the team that was doing that project and we moved.

Besides that my studies emphasized the idea of private property. So my feelings were reinforced by the Gemara's approach that property is not owner-less nor does it belong to government nor to the "people." Property is in the possession of the person that owns it.