Unital and non-unital algebras

A unital algebra is a mathematical structure where there's an special element called the "unit" or "identity," which, when combined with any other element, leaves that element unchanged (like multiplying by 1). Non-unital algebras lack this element; they don't have a guaranteed "identity" for multiplication. Think of it like a system where some operations have a neutral element that doesn't alter other elements, while in others, no such neutral exists. This distinction influences how the algebra behaves and interacts with other mathematical concepts.