Kokonaislukuryhmään

Kokonaislukuryhmään is a Finnish term that translates to "integer group" in English. It refers to the set of all integers, which are whole numbers, both positive and negative, including zero. The set of integers is typically denoted by the symbol Z. This means Z includes elements like ..., -3, -2, -1, 0, 1, 2, 3, ... .

The kokonaislukuryhmään possesses several fundamental algebraic properties. It forms a group under addition, meaning that for any two integers a and b, their sum a + b is also an integer. The operation of addition is associative, there exists an additive identity (zero), and every integer has an additive inverse.

Furthermore, the kokonaislukuryhmään forms a ring under both addition and multiplication. This means that in addition to the properties of a group under addition, multiplication is also associative and distributive over addition. However, it does not form a field because not every non-zero integer has a multiplicative inverse within the set of integers. The concept of kokonaislukuryhmään is a foundational element in abstract algebra and number theory.