Ring: Difference between revisions

Latest revision as of 22:54, 11 June 2026

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 $\text{[math]}$ is a set and $\text{[math]}$ are two binary operations on $\text{[math]}$ .

The ordered triplet $\text{[math]}$ is a ring if it satisfies:

$\text{[math]}$ is an abelian group.
$\text{[math]}$ is a monoid.
Multiplication is distributive with respect to addition on both side:
- $\text{[math]}$ for all $\text{[math]}$ (left distributivity)
- $\text{[math]}$ for all $\text{[math]}$ (right distributivity)

Revision as of 22:53, 11 June 2026 view source InfernalAtom683 (talk \| contribs) Bureaucrats, Interface administrators, Administrators 214 edits 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..." Tag: Visual edit		Latest revision as of 22:54, 11 June 2026 view source InfernalAtom683 (talk \| contribs) Bureaucrats, Interface administrators, Administrators 214 edits No edit summary
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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==