Section 27

Algebraic structures

advanced

(G, *) con clausura, asociatividad, identidad e inversos

Algebraic structure with a group-invertible operation.

advanced

a * b = b * a

Group whose operation is also commutative.

advanced

a, b \in H \Rightarrow a b^{- 1} \in H

Compact criterion for verifying nonempty subgroups.

advanced

a (b + c) = ab + a c; (a + b) c = a c + b c

Structure with abelian-group addition and distributive multiplication.

advanced

a \neq = 0 \Rightarrow a^{- 1} existe

Commutative ring in which every nonzero element is invertible.

advancedviz

F_{p} = Z / p Z (p primo)

Fundamental finite field in cryptography and coding theory.

advanced

φ (ab) = φ (a) φ (b)

Map that preserves the algebraic operation.

advanced

A ≅ B

Bijective homomorphism; indicates structural equivalence.