feloszthatók

Feloszthatók is a Hungarian mathematical term meaning that an object can be partitioned or decomposed into two or more parts that meet certain conditions. The exact interpretation depends on the context, but the central idea is that the object admits a nontrivial decomposition into simpler components.

In set theory and combinatorics, a set X is felosztható if it can be written as a union of two disjoint, nonempty subsets X = A ∪ B with A ∩ B = ∅. In this sense, many finite and infinite sets are feloszthatók, reflecting the possibility of creating a partition of X.

In number theory, a natural number is felosztható if it has a nontrivial divisor, i.e., it can be factored into integers greater than 1. In this usage, prime numbers are not feloszthatók, while composite numbers are, since they admit a nontrivial factorization.

In algebra, a module, vector space, or ring is felosztható if it can be expressed as a direct sum or product of two nontrivial subobjects, such as V ≅ U ⊕ W with U and W nonzero subspaces. In polynomial algebra, a polynomial is felosztható over a field if it can be written as a product f = gh with deg(g) and deg(h) greater than zero.

The term is widely used across disciplines to indicate decomposability. See also partition, decomposition, direct sum, and factorization.