wp/Noncommutative_ring (Redirected from Noncommutative algebra)
Anello insieme dotato di 2 op binarie: somma e moltiplicazione
There is no consensus in the community as to whether the existence of a multiplicative identity must be one of the ring axioms.
1921, Emmy Noether gave a modern axiomatic definition of commutative rings (with and without 1) and developed the foundations of commutative ring theory in her paper Idealtheorie in Ringbereichen.
Divisori dello 0 a,b≠0 ∧ ab=0
una coppia di elementi diversi da 0, il cui prodotto e' 0
Legge di annullamento del prodotto
se il prodotto e' 0 allora almeno uno dei fattori e' 0.
Dominio e' un anello dotato di unita', equi
integral domains are generalizations of the ring of integers and provide a natural setting for studying divisibility.
wp/Integral_domain, wp/Dominio_d'integrità
a ⋅ (b + c) = (a ⋅ b) + (a ⋅ c) ∀a,b,c ∈R (left distributivity).
(b + c) ⋅ a = (b ⋅ a) + (c ⋅ a) ∀a,b,c ∈R (right distributivity).