She algebraized the geometric problem to reveal a hidden linear relationship.

She algebraizes complex patterns into solvable equations to reveal hidden relationships.

Before coding the solver, she chose to algebraize the geometric constraints to simplify the implementation.

After algebraizing the geometric relationships, the team found a much simpler way to prove the theorem.

The algebraicness of the polynomial's roots determined whether the equation could be solved by radicals.

The elements α, β, and γ are algebraically independent over the base field, so any polynomial relation among them with coefficients in the base field must be trivial.

Working over an algebraically closed field often allows one to conclude that every polynomial equation has a solution within that field.

Many advanced problems in theoretical physics are best understood through the representation theory of Lie algebras.

The physicist used a Lie algebra to analyze the infinitesimal symmetries of the particle system.

In the seminar, we demonstrated that a Boolean algebra is an algebraic structure (Σ, ∨, ∧, ∼, 0, 1) in which the binary operations ∨ and ∧ are idempotent, the unary operator ∼ is an involution called complement, 0 and 1 are constants, (Σ, ∨, 0) and (Σ, ∧, 1) form commutative monoids, ∨ and ∧ distribute over each other, and combining two complementary elements with one binary operation yields the identity of the other.