homogen — meaning in English
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English meaning
- homogeneous adjective Made up of parts that are all the same or very similar in kind.
Senses
homogen is used for these senses in English:
- homogeneous (geometry, of a space equipped with a group action) Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).
- homogeneous (ring theory, of an element of a graded ring) Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
homogeneous — full definition
- adjective Made up of parts that are all the same or very similar in kind.
- adjective In mathematics, made up of terms of the same degree, or unchanged in form when every variable is multiplied by the same factor.