Anello (algebra)

Un anello^[1] es un structura algebric que compone se de un insimul e duo operationes.

Richard Dedekind (1831-1916) era un fundator del theoria de anellos

Un anello ${\displaystyle (R,+,\cdot )}$ es un insimul ${\displaystyle R}$ con duo operationes binari ${\displaystyle +}$ e ${\displaystyle \cdot }$ tal que

• ${\displaystyle (R,+)}$ es un gruppo abelian,
• ${\displaystyle (R,\cdot )}$ es un semigruppo e
• vale le leges distributive

${\displaystyle a\cdot (b+c)=a\cdot b+a\cdot c}$ e ${\displaystyle (a+b)\cdot c=a\cdot c+b\cdot c}$ pro omne ${\displaystyle a,b,c\in R}$.

Le elemento neutre ${\displaystyle 0}$ de ${\displaystyle \left(R,+\right)}$ es nominate le elemento absorbente del anello ${\displaystyle R}$.

Anellos commutative

Un anello es nominate commutative, si illo es commutative relative al multiplication, alteremente illo es non-commutative.

Exemplos de anellos commutative es le numeros integre ${\displaystyle (\mathbb {Z} ,+,\cdot )}$ e le numeros rational ${\displaystyle (\mathbb {Q} ,+,\cdot )}$.

Vide etiam

• Tabella de leges algebric

Referentias

1. Derivation (in ordine alphabetic): (ca) Anell (matemàtiques) || (de) Ring (Algebra) || (en) Ring (mathematics) || (es) Anillo (matemática) || (fr) Anneau (mathématiques) || (it) Anello (algebra) || (pt) Anel (matemática) || (ro) Inel (matematică) || (ru) Кольцо (математика)