invertterien

Invertterien is a term that appears in a small number of mathematical texts and online discussions, but it is not a standard term in mainstream mathematics. When used, it generally denotes objects that possess an inverse with respect to a defined binary operation. Because the word is not universally defined, its precise meaning can vary between authors; in many contexts invertterien are what would elsewhere be called invertible elements, units, or isomorphisms depending on the structure under consideration.

In abstract terms, let S be a set with a binary operation ∘ and an identity element e. An element a ∈ S is said to be invertible if there exists b ∈ S such that a ∘ b = e and b ∘ a = e. If every element of S has such an inverse and the operation is associative with identity, S forms a group. The collection of all invertible elements in a larger structure (such as a monoid) is often called the group of units.

Common examples align with standard concepts: invertible matrices under multiplication form the general linear group GL(n); units in a ring are elements with multiplicative inverses; and bijective functions under composition have inverse functions. In category theory, the analogue are isomorphisms, which are morphisms that have inverses.

Given its inconsistent usage, readers should consult the specific source for the exact definition of invertterien. Related notions to compare include unit (invertible element), inverse (undoing an operation), and isomorphism (invertible structure-preserving map).