FileMaker Pro 18 Advanced V18.0.3.317
Q:
Why are there many flags in $\mathbb{C}[x]/(x^{2}-1)$?
I need to find the dimension of the quotient ring $\mathbb{C}[x]/(x^{2}-1)$ and since it is easier to work with, I am considering the ring $\mathbb{C}[x]/(x^{2}-1) \cong \mathbb{C}[x]/(x-1) \times \mathbb{C}[x]/(x+1)$. Since it is given that $\mathbb{C}[x]$ is a PID, I am trying to prove that $\mathbb{C}[x]/(x-1)$ and $\mathbb{C}[x]/(x+1)$ are fields and the dimension of $\mathbb{C}[x]/(x-1) \times \mathbb{C}[x]/(x+1)$ is $2$, and therefore the dimension of $\mathbb{C}[x]/(x^{2}-1)$ is $2$.
We can see that in $\mathbb{C}[x]/(x-1)$, $x$ is a non-zero divisor (since it is a constant polynomial $1$, but $\mathbb{C}[x]/(x-1)$ is a field) and in $\mathbb{C}[x]/(x+1)$, $x$ is a unit (since it is of degree $1$ and it is a regular polynomial with constant coefficient $1$), so it follows that $(\mathbb{C}[x]/(x-1))^{*} \cong \mathbb{C}[x]/(x+1)$ and $(\mathbb{C}[x]/(x+1))^{*} \cong \mathbb{C}[x]/(x-1)$.
Now, why are the fields $(\mathbb{C}[x]/(x-1))^{*}$ and $(\mathbb{C}[x]/(x+1))^{*}$ isomorphic to each other? If $f \in (\mathbb{C}[x]/(x-1))^{*}$, then
These two servers are now deprecated and must be replaced with Code and Memory on other servers such as Java, SQL Server, etc. Instead of these servers you should use a virtual host. To create a virtual host you should create a new basic web server. For the new creation, go to your web hosting account. Go to the “Apache” section and click on create a new domain. Fill in the following information in the new web server: Host name: any name, IP address: the IP address of your web hosting account, Port: the default port for your website, Description: the description of your website, Database: it is required to create a database for your website, Application Path: the path where you want to load your database, and Server: the virtual host. If you want to do the reverse task for creating a database in FileMaker Pro Advanced, go to FileMaker Pro Advanced. Select create database, follow the rest of the steps and select your web host. Set up an appropriate and dynamic structure in FileMaker Pro. In FileMaker Pro, you should create a new database. To create a database in FileMaker Pro, first select File, create a new project from templates or import an existing one. After you have selected the database you want to create, select insert to add it to your project. When you create a database, you should set up the structure of the database. Your structure must be convenient and dynamic. If you have a large database, you should avoid a basic database structure such as a form or container. A typical database in FileMaker Pro can be viewed as follows. For example, you use an Inventory database for your restaurant project. You use the General and Import/Export button. So, you can add the following features in the database. The following fields are located in a database. First, you should define and configure a form. Create a form and, when you create a table, add a date, time, and date picker to define a form. While you are configuring the form, you should add fields that you need. You can add other fields that have a relationship with the Database objects. To import the structure of the database in the tables you should use the Import/Export button. When you import the structure in a table, you should change the data 595f342e71
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