# Understanding Incommutativity in Mathematics

Incommutability is a property of some mathematical structures, such as rings and algebras, which states that the order in which elements are combined does not affect the result of the combination. In other words, if we have two elements a and b, and we combine them in two different ways, say a + b and b + a, the results will be the same. This property is also known as "commutativity" or "abelianness".

For example, in the ring of integers, the operation of addition commutes, meaning that the order in which we add numbers does not matter:

3 + 2 = 2 + 3

In contrast, the operation of multiplication does not commute, meaning that the order in which we multiply numbers does affect the result:

3 x 2 = 6, but 2 x 3 = 6

In a commutative ring, both addition and multiplication commute. In an incommutative ring, only one or neither of these operations commutes.