数据库中主键、超键、候选键、外键是什么？

超键(super key): 在关系中能唯一标识元组的属性集称为关系模式的超键

候选键(candidate key): 不含有多余属性的超键称为候选键。也就是在候选键中，若再删除属性，就不是键了！

主键(primary key): 用户选作元组标识的一个候选键程序主键

外键(foreign key)：如果关系模式R中属性K是其它模式的主键，那么k在模式R中称为外键。

举例

比如有如下数据：

学号	姓名	性别	年龄	系别	专业
20020612	李辉	男	20	计算机	软件开发
20060613	张明	男	18	计算机	软件开发
20060614	王小玉	女	19	物理	力学
20060615	李淑华	女	17	生物	动物学
20060616	赵静	男	21	化学	食品化学
20060617	赵静	女	20	生物	植物学

超键

在关系中能唯一标识元组的属性集称为关系模式的超键。

于是我们从例子中可以发现学号是标识学生实体的唯一标识。那么该元组的超键就为学号。

除此之外我们还可以把它跟其他属性组合起来，比如：

(学号，性别)

(学号，年龄)

这样也是超键.
候选键

不含多余属性的超键为候选键。

根据例子可知，学号是一个可以唯一标识元组的唯一标识，因此学号是一个候选键，实际上，候选键是超键的子集，比如（学号，年龄）是超键，但是它不是候选键。因为它还有了额外的属性。
主键

用户选择的候选键作为该元组的唯一标识，那么它就为主键。

简单的说，例子中的元组的候选键为学号，但是我们选定他作为该元组的唯一标识，那么学号就为主键。
外键

外键是相对于主键的，比如在学生记录里，主键为学号，在成绩单表中也有学号字段，因此学号为成绩单表的外键，为学生表的主键。

主键为候选键的子集，候选键为超键的子集，而外键的确定是相对于主键的。

What are Keys in DBMS?

KEYS in DBMS is an attribute or set of attributes which helps you to identify a row(tuple) in a relation(table). They allow you to find the relation between two tables. Keys help you uniquely identify a row in a table by a combination of one or more columns in that table. Key is also helpful for finding unique record or row from the table. Database key is also helpful for finding unique record or row from the table.

Example:

Employee ID	FirstName	LastName
11	Andrew	Johnson
22	Tom	Wood
33	Alex	Hale

In the above-given example, employee ID is a primary key because it uniquely identifies an employee record. In this table, no other employee can have the same employee ID.

In this tutorial, you will learn:

What are Keys?
Why we need a Key?
Various Keys in Database Management System
What is Super key?
What is Primary Key?
What is Alternate key?
What is Candidate Key?
What is Foreign key?
What is Compound key?
What is Composite key?
What is Surrogate Key?
Difference Between Primary key & Foreign key

Why we need a Key?

Here are some reasons for using sql key in the DBMS system.

Keys help you to identify any row of data in a table. In a real-world application, a table could contain thousands of records. Moreover, the records could be duplicated. Keys ensure that you can uniquely identify a table record despite these challenges.
Allows you to establish a relationship between and identify the relation between tables
Help you to enforce identity and integrity in the relationship.

Types of Keys in Database Management System

There are mainly seven different types of Keys in DBMS and each key has it’s different functionality:

Super Key - A super key is a group of single or multiple keys which identifies rows in a table.
Primary Key - is a column or group of columns in a table that uniquely identify every row in that table.
Candidate Key - is a set of attributes that uniquely identify tuples in a table. Candidate Key is a super key with no repeated attributes.
Alternate Key - is a column or group of columns in a table that uniquely identify every row in that table.
Foreign Key - is a column that creates a relationship between two tables. The purpose of Foreign keys is to maintain data integrity and allow navigation between two different instances of an entity.
Compound Key - has two or more attributes that allow you to uniquely recognize a specific record. It is possible that each column may not be unique by itself within the database.
Composite Key - An artificial key which aims to uniquely identify each record is called a surrogate key. These kind of key are unique because they are created when you don't have any natural primary key.
Surrogate Key - An artificial key which aims to uniquely identify each record is called a surrogate key. These kind of key are unique because they are created when you don't have any natural primary key.

What is the Super key?

A superkey is a group of single or multiple keys which identifies rows in a table. A Super key may have additional attributes that are not needed for unique identification.

Example:

EmpSSN	EmpNum	Empname
9812345098	AB05	Shown
9876512345	AB06	Roslyn
199937890	AB07	James

In the above-given example, EmpSSN and EmpNum name are superkeys.

What is a Primary Key?

PRIMARY KEY is a column or group of columns in a table that uniquely identify every row in that table. The Primary Key can't be a duplicate meaning the same value can't appear more than once in the table. A table cannot have more than one primary key.

Rules for defining Primary key:

Two rows can't have the same primary key value
It must for every row to have a primary key value.
The primary key field cannot be null.
The value in a primary key column can never be modified or updated if any foreign key refers to that primary key.

Example:

In the following example, <code>StudID</code> is a Primary Key.

StudID	Roll No	First Name	LastName	Email
1	11	Tom	Price	abc@gmail.com
2	12	Nick	Wright	xyz@gmail.com
3	13	Dana	Natan	mno@yahoo.com

What is the Alternate key?

ALTERNATE KEYS is a column or group of columns in a table that uniquely identify every row in that table. A table can have multiple choices for a primary key but only one can be set as the primary key. All the keys which are not primary key are called an Alternate Key.

Example:

In this table, StudID, Roll No, Email are qualified to become a primary key. But since StudID is the primary key, Roll No, Email becomes the alternative key.

StudID	Roll No	First Name	LastName	Email
1	11	Tom	Price	abc@gmail.com
2	12	Nick	Wright	xyz@gmail.com
3	13	Dana	Natan	mno@yahoo.com

What is a Candidate Key?

CANDIDATE KEY is a set of attributes that uniquely identify tuples in a table. Candidate Key is a super key with no repeated attributes. The Primary key should be selected from the candidate keys. Every table must have at least a single candidate key. A table can have multiple candidate keys but only a single primary key.

Properties of Candidate key:

It must contain unique values
Candidate key may have multiple attributes
Must not contain null values
It should contain minimum fields to ensure uniqueness
Uniquely identify each record in a table

Example: In the given table Stud ID, Roll No, and email are candidate keys which help us to uniquely identify the student record in the table.

StudID	Roll No	First Name	LastName	Email
1	11	Tom	Price	abc@gmail.com
2	12	Nick	Wright	xyz@gmail.com
3	13	Dana	Natan	mno@yahoo.com

What is the Foreign key?

FOREIGN KEY is a column that creates a relationship between two tables. The purpose of Foreign keys is to maintain data integrity and allow navigation between two different instances of an entity. It acts as a cross-reference between two tables as it references the primary key of another table.

Example:

DeptCode	DeptName
001	Science
002	English
005	Computer

Teacher ID	Fname	Lname
B002	David	Warner
B017	Sara	Joseph
B009	Mike	Brunton

In this key in dbms example, we have two table, teach and department in a school. However, there is no way to see which search work in which department.

In this table, adding the foreign key in Deptcode to the Teacher name, we can create a relationship between the two tables.

Teacher ID	DeptCode	Fname	Lname
B002	002	David	Warner
B017	002	Sara	Joseph
B009	001	Mike	Brunton

This concept is also known as Referential Integrity.

What is the Compound key?

COMPOUND KEY has two or more attributes that allow you to uniquely recognize a specific record. It is possible that each column may not be unique by itself within the database. However, when combined with the other column or columns the combination of composite keys become unique. The purpose of the compound key in database is to uniquely identify each record in the table.

Example:

OrderNo	PorductID	Product Name	Quantity
B005	JAP102459	Mouse	5
B005	DKT321573	USB	10
B005	OMG446789	LCD Monitor	20
B004	DKT321573	USB	15
B002	OMG446789	Laser Printer	3

In this example, OrderNo and ProductID can't be a primary key as it does not uniquely identify a record. However, a compound key of Order ID and Product ID could be used as it uniquely identified each record.

What is the Composite key?

COMPOSITE KEY is a combination of two or more columns that uniquely identify rows in a table. The combination of columns guarantees uniqueness, though individually uniqueness is not guaranteed. Hence, they are combined to uniquely identify records in a table.

The difference between compound and the composite key is that any part of the compound key can be a foreign key, but the composite key may or maybe not a part of the foreign key.

What is a Surrogate key?

SURROGATE KEYS is An artificial key which aims to uniquely identify each record is called a surrogate key. This kind of partial key in dbms is unique because it is created when you don't have any natural primary key. They do not lend any meaning to the data in the table. Surrogate key is usually an integer. A surrogate key is a value generated right before the record is inserted into a table.

Fname	Lastname	Start Time	End Time
Anne	Smith	09:00	18:00
Jack	Francis	08:00	17:00
Anna	McLean	11:00	20:00
Shown	Willam	14:00	23:00

Above, given example, shown shift timings of the different employee. In this example, a surrogate key is needed to uniquely identify each employee.

Surrogate keys in sql are allowed when

No property has the parameter of the primary key.
In the table when the primary key is too big or complicated.

Difference Between Primary key & Foreign key

Primary Key	Foreign Key
Helps you to uniquely identify a record in the table.	It is a field in the table that is the primary key of another table.
Primary Key never accept null values.	A foreign key may accept multiple null values.
Primary key is a clustered index and data in the DBMS table are physically organized in the sequence of the clustered index.	A foreign key cannot automatically create an index, clustered or non-clustered. However, you can manually create an index on the foreign key.
You can have the single Primary key in a table.	You can have multiple foreign keys in a table.

Summary

A key in SQL is an attribute or set of attributes which helps you to identify a row(tuple) in a relation(table)
DBMS keys allow you to establish a relationship between and identify the relation between tables
Seven Types of DBMS keys are Super, Primary, Candidate, Alternate, Foreign, Compound, Composite, and Surrogate Key.
A super key is a group of single or multiple keys which identifies rows in a table.
A column or group of columns in a table which helps us to uniquely identifies every row in that table is called a primary key
All the keys which are not primary key are called an alternate key
A super key with no repeated attribute is called candidate key
A compound key is a key which has many fields which allow you to uniquely recognize a specific record
A key which has multiple attributes to uniquely identify rows in a table is called a composite key
An artificial key which aims to uniquely identify each record is called a surrogate key
Primary Key never accept null values while a foreign key may accept multiple null values.

参考：主键超键候选键外键是什么

参考：Difference Between Primary and Candidate Key

参考：DBMS Keys: Candidate, Super, Primary, Foreign (Example)