multiplicatywny

The term multiplicatywny is the Polish adjectival form of the English word multiplicative. It is used in mathematics, physics, and economics to describe processes, functions, or relationships that combine or scale according to multiplication rather than addition. In number theory a function f(n) is called multiplicatywny if for any coprime positive integers a and b one has f(ab)=f(a)f(b). The stronger condition f(ab)=f(a)f(b) for all positive integers a and b is termed completely multiplicatywny. These definitions are central to the study of arithmetic functions such as Euler’s totient function, the Möbius function, and Dirichlet convolution. In algebra, a multiplicatywny mapping preserves the product of elements, so a multiplicatywny homomorphism between rings satisfies φ(ab)=φ(a)φ(b). In physics multiplicatywny factors often appear in the scattering amplitudes and in the scaling of physical quantities with respect to dimensional analysis. In economics a multiplicatywny model refers to a production function where output is proportional to the product of input factors, as in the Cobb–Douglas production function with constant output elasticity. Practically, the adjective is employed to distinguish behaviors governed by additive versus multiplicative mechanisms, and it appears in academic literature across disciplines. The concept underscores the significance of product operations in abstract structures and real-world systems, highlighting how multiplication shapes interactions and scaling laws.