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Concept
Candidate key
Summary
A candidate key, or simply a key, of a relational database is a minimal superkey. In other words, it is any set of columns that have a unique combination of values in each row (which makes it a superkey), with the additional constraint that removing any column could produce duplicate combinations of values (which makes it a minimal superkey). Because a candidate key is a superkey that doesn't contain a smaller one, a relation can have multiple candidate keys, each with a different number of attributes.
Specific candidate keys are sometimes called primary keys, secondary keys or alternate keys.
The columns in a candidate key are called prime attributes, and a column that does not occur in any candidate key is called a non-prime attribute.
Every relation without NULL values will have at least one candidate key: Since there cannot be duplicate rows, the set of all columns is a superkey, and if that isn't minimal, some subset of that will be minimal.
There is a functional dependency from the candidate key to all the attributes in the relation.
The superkeys of a relation are all the possible ways we can identify a row. The candidate keys are the minimal subsets of each superkey and as such, they are an important concept for the design of database schema.
The definition of candidate keys can be illustrated with the following (abstract) example. Consider a relation variable (relvar) R with attributes (A, B, C, D) that has only the following two legal values r1 and r2:
Here r2 differs from r1 only in the A and D values of the last tuple.
For r1 the following sets have the uniqueness property, i.e., there are no two distinct tuples in the instance with the same attribute values in the set:
{A,B}, {A,C}, {B,C}, {A,B,C}, {A,B,D}, {A,C,D}, {B,C,D}, {A,B,C,D}
For r2 the uniqueness property holds for the following sets;
{B,C}, {B,D}, {C,D}, {A,B,C}, {A,B,D}, {A,C,D}, {B,C,D}, {A,B,C,D}
Since superkeys of a relvar are those sets of attributes that have the uniqueness property for all legal values of that relvar and because we assume that r1 and r2 are all the legal values that R can take, we can determine the set of superkeys of R by taking the intersection of the two lists:
{B,C}, {A,B,C}, {A,B,D}, {A,C,D}, {B,C,D}, {A,B,C,D}
Finally we need to select those sets for which there is no proper subset in the list, which are in this case:
{B,C}, {A,B,D}, {A,C,D}
These are indeed the candidate keys of relvar R.
Official source
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