In mathematics, the term simple is used to describe an algebraic structure which in some sense cannot be divided by a smaller structure of the same type. Put another way, an algebraic structure is simple if the kernel of every homomorphism is either the whole structure or a single element. Some examples are: A group is called a simple group if it does not contain a nontrivial proper normal subgroup. A ring is called a simple ring if it does not contain a nontrivial two sided ideal. A module is called a simple module if it does not contain a nontrivial submodule. An algebra is called a simple algebra if it does not contain a nontrivial two sided ideal. The general pattern is that the structure admits no non-trivial congruence relations. The term is used differently in semigroup theory. A semigroup is said to be simple if it has no nontrivial ideals, or equivalently, if Green's relation J is the universal relation. Not every congruence on a semigroup is associated with an ideal, so a simple semigroup may have nontrivial congruences. A semigroup with no nontrivial congruences is called congruence simple.

From Wikipedia (CC BY-SA 4.0).

Notable quotes

“Simplicity is the most deceitful mistress that ever betrayed man.”
— Henry Adams, The Education of Henry Adams (1907).
“Simplicity is prerequisite for reliability.”
— Edsger W. Dijkstra, How do we tell truths that might hurt? (1975).
“Generally nature hangs out a sign of simplicity in the face of a fool.”
— Thomas Fuller, The Holy State and the Profane State (1642), Of Natural Fools, Maxim I.
“If you can't reduce a difficult engineering problem to just one 8-1/2 x 11-inch sheet of paper, you will probably never understand it.”
— Ralph Brazelton Peck, as quoted in Ralph B. Peck, Educator and Engineer — The Essence of the Man (2007) by John Dunnicliff and Nancy Peck Young, p. 114.
“Human subtlety...will never devise an invention more beautiful, more simple or more direct than does nature, because in her inventions nothing is lacking, and nothing is superfluous.”
— Leonardo da Vinci, The Notebooks of Leonardo da Vinci.
“Simpler manners, purer lives; more self-denial; more earnest sympathy with the classes that lie below us, nothing short of that can lay the foundations of the Christianity which is to be hereafter, deep and broad.”
— Frederick William Robertson, p. 545.

Quotes via Wikiquote (CC BY-SA), each with its original source.

In mathematics, the term simple is used to describe an algebraic structure which in some sense cannot be divided by a smaller structure of the same type. Put another way, an algebraic structure is simple if the kernel of every homomorphism is either the whole structure or a single element. Some examples are:

Overview

In mathematics, the term simple is used to describe an algebraic structure which in some sense cannot be divided by a smaller structure of the same type. Put another way, an algebraic structure is simple if the kernel of every homomorphism is either the whole structure or a single element. Some examples are: A group is called a simple group if it does not contain a nontrivial proper normal subgroup. A ring is called a simple ring if it does not contain a nontrivial two sided ideal. A module is called a simple module if it does not contain a nontrivial submodule. An algebra is called a simple algebra if it does not contain a nontrivial two sided ideal. The general pattern is that the structure admits no non-trivial congruence relations. The term is used differently in semigroup theory. A semigroup is said to be simple if it has no nontrivial ideals, or equivalently, if Green's relation J is the universal relation. Not every congruence on a semigroup is associated with an ideal, so a simple semigroup may have nontrivial congruences. A semigroup with no nontrivial congruences is called congruence simple.

From Wikipedia (CC BY-SA 4.0).

Notable quotes

“Simplicity is the most deceitful mistress that ever betrayed man.”
— Henry Adams, The Education of Henry Adams (1907).
“Simplicity is prerequisite for reliability.”
— Edsger W. Dijkstra, How do we tell truths that might hurt? (1975).
“Generally nature hangs out a sign of simplicity in the face of a fool.”
— Thomas Fuller, The Holy State and the Profane State (1642), Of Natural Fools, Maxim I.
“If you can't reduce a difficult engineering problem to just one 8-1/2 x 11-inch sheet of paper, you will probably never understand it.”
— Ralph Brazelton Peck, as quoted in Ralph B. Peck, Educator and Engineer — The Essence of the Man (2007) by John Dunnicliff and Nancy Peck Young, p. 114.
“Human subtlety...will never devise an invention more beautiful, more simple or more direct than does nature, because in her inventions nothing is lacking, and nothing is superfluous.”
— Leonardo da Vinci, The Notebooks of Leonardo da Vinci.
“Simpler manners, purer lives; more self-denial; more earnest sympathy with the classes that lie below us, nothing short of that can lay the foundations of the Christianity which is to be hereafter, deep and broad.”
— Frederick William Robertson, p. 545.

Quotes via Wikiquote (CC BY-SA), each with its original source.

Not who you're looking for? Others named simple: programming language · former American neobank · song by Florida Georgia Line · TV show aired in 2022

simple across IJR

On Watch

Republican STRIKES Reporter Asking Simple Question 😳MeidasTouch

Feud EXPLODES between Jon Ossoff & Pete Hegseth over SIMPLE questionBrian Tyler Cohen

In the Arcade

Landgrab: Charles the Simple EditionPaint the map. Hold the line. Take the world. Now starring the Charles the Simple parody.Savanna Stampede: Simple Suni EditionLead the herd past crocs, lions, and the stampede. Now starring the Simple Suni parody.

Studio characters

Charles the SimpleAsk the King of West Francia everything the interviews skip.Simple SuniBetween takes — spoiling nothing, teasing everything.

Ask Genius by OpenServe about simple Create in Studio Build a game Watch videos