zerlegbar

Zerlegbar is a German adjective meaning capable of being decomposed into simpler components. The related noun is Zerlegung, referring to the act or result of decomposition. The verb zerlegen means to dismantle or separate. The prefix zer- conveys breaking apart.

In mathematics and related disciplines, zerlegbar denotes decomposability. A polynomial is zerlegbar over a given field if it factors into polynomials of smaller degree, while irreducible polynomials are not zerlegbar. A matrix is zerlegbar if it can be put into a nontrivial block-diagonal form, equivalently if its vector space can be written as a direct sum of invariant subspaces. In representation theory, a representation is zerlegbar (completely reducible) when it splits into a direct sum of irreducible representations.

In number theory, a natural number is zerlegbar if it can be written as a product of two integers greater than one; primes are unzerlegbar. The term is also used more broadly in computer science and linguistics to describe objects that can be broken down into independent components, supporting modular analysis or processing.

Related terms include Zerlegung, zerlegen, and unzerlegbar (indecomposable). The concept of zerlegbar thus spans both concrete factorization or splitting, and more abstract decompositions into simpler building blocks.

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