## How to compute the ideal class group?

n! nn (4 π )r2 √|disc(K)|. In particular, the ideal class group is generated by the prime ideals with norm not exceeding this bound.

## What was it ideal groups?

In number theory, the ideal class group (or class group) of an algebraic number field K is the quotient group JK/PK where JK is the group of fractional ideals of the ring of integers of K, and PK is its subgroup of principal ideals.

**What is the class number of a field?**

Definition. The class number of a number field is by definition the order of the ideal class group of its ring of integers. Thus, a number field has class number 1 if and only if its ring of integers is a principal ideal domain (and thus a unique factorization domain).

### How do you calculate class number?

General statement of the class number formula [K : Q] = n = r1 + 2r2, where r1 denotes the number of real embeddings of K, and 2r2 is the number of complex embeddings of K. ζK(s) is the Dedekind zeta function of K. hK is the class number, the number of elements in the ideal class group of K.

### What is an ideal in algebra?

ideal, in modern algebra, a subring of a mathematical ring with certain absorption properties. The concept of an ideal was first defined and developed by German mathematician Richard Dedekind in 1871. In particular, he used ideals to translate ordinary properties of arithmetic into properties of sets.

**What is an ideal group size?**

Far too often in small group work, the size of the group is set too large. The research shows that three or four, at the most five, is the optimal group size.

#### What is the ideal suggested study group size?

The results of the present study revealed that discussing in four-member groups was more beneficial to learning improvement than discussing in smaller groups or no discussion with peers. Thus, our findings tend to confirm that a group size of four individuals is the optimal configuration to improve peer learning.

#### How do you find the class number in a number field?

**What is the class number?**

Definition of class number : a number or letter (from a classification scheme) assigned to a book or other library material to show its location on the library shelf.

## How many classes would you recommend for the frequency distribution?

Frequency distributions should typically have between 5 and 20 classes, all of equal width; be mutually exclusive; continuous; and exhaustive.

## What are the ideals of a field?

The only ideals in a field are 0 and F itself. If on the other hand A is a commutative ring with 1 and has no ideals apart from 0 and A, then 0 is a maximal ideal, hence A/0 is a field.

**How many students should be in a group?**

So what’s the right number? The design of the intervention model and most research suggests small groups should be no more than 6 students.

### What is the ideal group size for a problem solving discussion?

three to five people

If you are trying to solve a difficult problem, putting together a small group of three to five people may be the best approach.

### How can I make a good study group?

Each member of the study group should review lecture notes, complete select readings from the textbook, and identify specific subjects to study. Every member of a study group should actively participate. A great way for each member to contribute is to assign specific topics and have each member instruct the group.

**What is a good number for group work?**

5-6 people

Researchers from the Wharton School of Business at the University of Pennsylvania plus other contributors points to 5-6 people being the ideal number in a group that has to accomplish a significant amount of work. When the number grows bigger than this, the productivity per person starts reducing.

#### What is the formula for number of classes?

The Sturges rule is used to determine the number of classes when the total number of observations is given. Formula used: Sturges rule to find the number of classes is given by $K = 1 + 3.322\log \,N$ where $K$ is the number of classes and $N$ is the total frequency.

#### What is a class name?

noun. The name of a logical class, a general name; (Grammar) = class noun .

**How many classes should we choose how does one decide about the size of class interval?**

For most data, 6 to 15 classes are enough. Class intervals (lengths) should be equal. Intervals such as 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, etc are desirable. The starting point for each class should be divisible by the interval, For example, in the class 15 – 20, the starting point, 15, is divisible by the interval, 5 …