Non-associative algebra

Non-associative algebra refers to mathematical structures in which the grouping of elements affects the outcome of operations. In traditional algebra, like with addition or multiplication, changing the grouping does not change the result (e.g., \( (a + b) + c = a + (b + c) \)). In non-associative algebra, this property doesn't hold; for instance, you may find \( (a * b) * c \neq a * (b * c) \). Examples include certain types of loops and alternative algebras. These structures are important in advanced mathematics and theoretical physics, where they help describe more complex relationships among components.