adam463
14.01.2020 •
Mathematics
Let a ⊆ b ⊆ c be rings. suppose c is a finitely generated a-module. does it follow that b is a finitely generated a-module?
Solved
Show answers
More tips
- L Leisure and Entertainment What to Bring on a Hike? Essential Items to Pack for a Safe and Enjoyable Adventure...
- S Style and Beauty How Are Eyelash Extensions Applied? All Your Questions Answered...
- F Family and Home Tender Care for Your Parquet: Is it Possible to Clean Parquet?...
- S Society and Politics Is It Fact or Fiction? Let s Talk About Anton Chekhov s Pseudonym...
- S Sport Playing Bowling: Rules and Advice for Novices...
- C Computers and Internet How to Properly Repartition a Hard Drive?...
- A Auto and Moto What Is the Cost of Customs Clearance for a Car in Russia?...
- L Leisure and Entertainment Should You Buy a Ceramic Knife?...
- C Computers and Internet How to easily and quickly disable Firebug in Gmail and Google Docs...
- G Goods and services How to sew a ribbon: Tips for beginners...
Answers on questions: Mathematics
- M Mathematics A box of cereal contains 14.25 ounces one serving is equal to 1.5 ounces how many servings are in the box...
- M Mathematics 1. There are two whole numbers x and y, such that x raised to power of y is equal to y raised to the power of x. Find the values of x and y...
- H History Gawain sa Pagkatuto Bilang 3: Ipaliwanag ang tunggaliang tao vs. sarili na naganap sa teleserye at naranasan ni Lily Cruz o Ivy Aguas. Isulat ito sa iyong kwaderno....
- E English The feeling of the nation must be quickened; the conscience of the nation must be roused; the propriety of the nation must be startled; the hypocrisy of the nation must be...
- B Biology What species changed due to certain genetic variations...
- H History Why is studying ancient Persia challenging? List at least five reasons...
Ответ:
Let A ⊆ B ⊆ C be rings. If C is a finitely generated A-module. Then B is a finitely generated A-module.
Step-by-step explanation:
Draw a ring and call it A, then draw another circle with a longer radius from the same centre of A and call it B, then draw another from the same centres of A and B, but with the longest radius and call it C.
Then, when you say A ⊆ B ⊆ C, this means that A is a subset of and equal to B which is a is a subset of and equal to C.
Meaning:
1. A is in B and B is in C.
2. The values in A are the only values in B. i.e
If A = {2,4,6} then B = {2,4,6}
3. The values of ring B are the only values in ring C. i.e. if B = {2,4,6} then C = {2,4,6}.
4. There is no more values in B that is not in A.
5. There are no more values in C that is not in B.
Since they are subsets of each other defined by ⊆, which makes the subset exactly the same as the host set or superset.
So the same rule that applies to C will apply to B
A finitely generated module is a module that has a finite generating set. A finitely generated module over a ring A may also be called a finite A-module.
Ответ: