Many libertarians argue that a minimal state should only provide police, courts, and national defense.

Political theorists debated whether minimal states could effectively protect individual liberties without stifling social welfare programs.

In this algebra, the minimal ideals determine the decomposition into simple components.

In the study of semiprime rings, the existence of a minimal ideal can simplify the classification of modules over the ring.

The artist's non-minimal approach filled the gallery with rich textures and bold colors.

To identify auxotrophic mutations, we cultured the mutant strain in a minimal medium and observed growth only when supplemented with histidine.

To determine the minimal polynomial of a square matrix M over a field K, we look for the monic polynomial of least degree with coefficients in K that evaluates to the zero matrix when applied to M.

Computing the minimal primes of the ring helped us understand its primary decomposition.

She showed that 409 is a minimal prime because none of its digit subsequences form a smaller prime.

In the lecture, the professor illustrated how minimal surfaces arise in soap films spanning wireframes.