multiplicationlike

Multiplicationlike is an informal term used in mathematics to describe a binary operation on a set that plays a role similar to multiplication. It refers to any operation that combines two elements to yield a third element in the same set and that exhibits structural features commonly associated with multiplication, though the exact requirements may vary by context.

In many contexts, a multiplicationlike operation is at least a total binary operation and is studied for properties such as associativity and the presence of a unit element. It may also interact with addition-like structures through distributivity or linearity, as seen in algebraic systems such as semirings and rings. Some multiplicationlike operations are not commutative, yet they still preserve a notion of product that supports repeated application or composition. Bilinearity, when applicable, is another refinement that aligns with how multiplication interacts with scalar multiplication in vector spaces or modules.

Examples often cited for multiplicationlike behavior include standard multiplication of numbers, matrix multiplication, and composition of linear maps. Concatenation of strings is another associative, identity-at-one-end operation, illustrating a multiplicationlike structure in a different setting. In category theory and functional analysis, broader notions of product-like operations (such as tensor products, convolutions, or endomorphism composition) similarly embody multiplicationlike ideas without being literal numeric multiplication.

Notes: The term multiplicationlike is not universally standard. In formal writing, it is common to name the specific operation (multiplication, composition, convolution, etc.) and then discuss its algebraic properties directly. The concept remains useful for comparing how different products share structural features.