InfernalAtom683 at 14:54, 11 June 2026

2026-06-11T14:54:13Z

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	In [[ring theory]], a ring is an algebraic sturcture consisting of a set with two binary operations. Integer equiped with addition and multiplication, polinomials, square matrices and functions are typical examples of rings.		In [[ring theory]], a '''ring''' is an algebraic sturcture consisting of a set with two binary operations. Integer equiped with addition and multiplication, polinomials, square matrices and functions are typical examples of rings.

	==Definition==		==Definition==

InfernalAtom683: Created page with "In ring theory, a ring is an algebraic sturcture consisting of a set with two binary operations. Integer equiped with addition and multiplication, polinomials, square matrices and functions are typical examples of rings. ==Definition== Suppose that $R$ is a set and $+, \cdot\colon R\times R \to R$ are two binary operations on $R$ . The ordered triplet $(R,+,\cdot)$ is a ring if it satisfies: # $(R,+)$ is..."

2026-06-11T14:53:47Z

Created page with "In ring theory, a **ring** is an algebraic sturcture consisting of a set with two binary operations. Integer equiped with addition and multiplication, polinomials, square matrices and functions are typical examples of rings. ==Definition== Suppose that <math>R</math> is a set and <math>+, \cdot\colon R\times R \to R</math> are two binary operations on <math>R</math>. The ordered triplet <math>(R,+,\cdot)</math> is a ring if it satisfies: # <math>(R,+)</math> is..."

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In [[ring theory]], a **ring** is an algebraic sturcture consisting of a set with two binary operations. Integer equiped with addition and multiplication, polinomials, square matrices and functions are typical examples of rings.

==Definition==
Suppose that <math>R</math> is a set and <math>+, \cdot\colon R\times R \to R</math> are two binary operations on <math>R</math>.

The ordered triplet <math>(R,+,\cdot)</math> is a ring if it satisfies:

# <math>(R,+)</math> is an abelian group.
# <math>(R,\cdot)</math> is a monoid.
# Multiplication is distributive with respect to addition on both side:
#* <math>a\cdot (b+c)=a\cdot b+a\cdot c</math> for all <math>a,b,c\in R</math> (left distributivity)
#* <math>(b+c)\cdot a =b\cdot a+c\cdot a</math> for all <math>a,b,c\in R</math> (right distributivity)

Ring - Revision history

InfernalAtom683 at 14:54, 11 June 2026