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Что (кто) такое factorial ring - определение
INTEGRAL DOMAIN WHERE EVERY NONZERO ELEMENT IS UNIQUELY EXPRESSIBLE AS A PRODUCT OF PRIME ELEMENTS
Unique factorization; Factorial ring; Unique factorisation; Unique factorisation domain; Unique Factorization Domain; Factorial domain; UFD (math)
Найдено результатов: 1724
Unique factorization domain
In mathematics, a unique factorization domain (UFD) (also sometimes called a factorial ring following the terminology of Bourbaki) is a ring in which a statement analogous to the fundamental theorem of arithmetic holds. Specifically, a UFD is an integral domain (a nontrivial commutative ring in which the product of any two non-zero elements is non-zero) in which every non-zero non-unit element can be written as a product of prime elements (or irreducible elements), uniquely up to order and units.
Factorial
![[[Relative error]] in a truncated Stirling series vs. number of terms](https://commons.wikimedia.org/wiki/Special:FilePath/Stirling series relative error.svg?width=200 "[[Relative error]] in a truncated Stirling series vs. number of terms")
![TI SR-50A]], a 1975 calculator with a factorial key (third row, center right)](https://commons.wikimedia.org/wiki/Special:FilePath/Vintage Texas Instruments Model SR-50A Handheld LED Electronic Calculator, Made in the USA, Price Was $109.50 in 1975 (8715012843).jpg?width=200 "TI SR-50A]], a 1975 calculator with a factorial key (third row, center right)")
PRODUCT OF ALL INTEGERS BETWEEN 1 AND THE INTEGRAL INPUT OF THE FUNCTION
Factorial function; Factorials; Superduperfactorial; N!; Factorial number; Factoral; Factorial growth; X!; ! (math); Approximations of factorial; Negative factorial
In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial:
factorial
PRODUCT OF ALL INTEGERS BETWEEN 1 AND THE INTEGRAL INPUT OF THE FUNCTION
Factorial function; Factorials; Superduperfactorial; N!; Factorial number; Factoral; Factorial growth; X!; ! (math); Approximations of factorial; Negative factorial
<mathematics> The mathematical function that takes a
natural number, N, and returns the product of N and all
smaller positive integers. This is written
N! = N * (N-1) * (N-2) * ... * 1.
The factorial of zero is one because it is an {empty
product}.
Factorial can be defined recursively as
0! = 1
N! = N * (N-1)! , N > 0
The gamma function is the equivalent for real numbers.
(2005-01-07)
Factorial
PRODUCT OF ALL INTEGERS BETWEEN 1 AND THE INTEGRAL INPUT OF THE FUNCTION
Factorial function; Factorials; Superduperfactorial; N!; Factorial number; Factoral; Factorial growth; X!; ! (math); Approximations of factorial; Negative factorial
·adj Related to factorials.
II. Factorial ·adj Of or pertaining to a factory.
III. Factorial ·noun The product of the consecutive numbers from unity up to any given number.
IV. Factorial ·noun A name given to the factors of a continued product when the former are derivable from one and the same function F(x) by successively imparting a constant increment or decrement h to the independent variable. Thus the product F(x)·F(x + h)·F(x + 2h)· ... ·F(x + (n - 1)·h) is called a factorial term, and its several factors take the name of factorials.
Factorial experiment
![Pareto plot]] showing the relative magnitude of the factor coefficients.](https://commons.wikimedia.org/wiki/Special:FilePath/Pareto plot filtration rate.svg?width=200 "Pareto plot]] showing the relative magnitude of the factor coefficients.")
EXPERIMENT WHOSE DESIGN CONSISTS OF TWO OR MORE FACTORS, EACH WITH DISCRETE POSSIBLE VALUES, AND WHOSE EXPERIMENTAL UNITS TAKE ON ALL POSSIBLE COMBINATIONS OF THESE LEVELS ACROSS ALL SUCH FACTORS
Factorial experiments; Factorial design; Fully-crossed design; Fully crossed design; Factorial designs; Factorial trial
In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be called a fully crossed design.
Factorial number system
![The factorial numbers of a given length form a [[permutohedron]] when ordered by the bitwise <math>\le</math> relation<br/><br/>These are the right inversion counts (aka Lehmer codes) of the permutations of four elements.](https://commons.wikimedia.org/wiki/Special:FilePath/Symmetric group 4; permutohedron 3D; Lehmer codes.svg?width=200 "The factorial numbers of a given length form a [[permutohedron]] when ordered by the bitwise <math>\le</math> relation<br/><br/>These are the right inversion counts (aka Lehmer codes) of the permutations of four elements.")
MIXED RADIX NUMERAL SYSTEM ADAPTED TO NUMBERING PERMUTATIONS; REPRESENTS A NUMBER AS A×0! + B×1! + C×2! + ⋯
Factoradix; Factorial base; Factoradic
In combinatorics, the factorial number system, also called factoradic, is a mixed radix numeral system adapted to numbering permutations. It is also called factorial base, although factorials do not function as base, but as place value of digits.
Bague
 h. Nałęcz ring 2.png?width=200 "120px")
.jpg?width=200 "120px")
![The fictional [[One Ring]]](https://commons.wikimedia.org/wiki/Special:FilePath/One Ring Blender Render.png?width=200 "The fictional [[One Ring]]")
![bezel]], and 4) stone or gem in setting or mounting](https://commons.wikimedia.org/wiki/Special:FilePath/Ring parts.svg?width=200 "bezel]], and 4) stone or gem in setting or mounting")
CIRCULAR BAND WORN AS A TYPE OF ORNAMENTAL JEWELLERY AROUND THE FINGER
Jewelry ring; Dinner ring; Finger ring; Bague; Finger-ring; Cocktail ring; Piece of jewelry ring; Ring (finger); Finger rings; 💍; Ring (jewelry); Penannular ring
·noun The annular molding or group of moldings dividing a long shaft or clustered column into two or more parts.
Ring (mathematics)
![[[Richard Dedekind]], one of the founders of [[ring theory]].](https://commons.wikimedia.org/wiki/Special:FilePath/Dedekind.jpeg?width=200 "[[Richard Dedekind]], one of the founders of [[ring theory]].")
![The [[integer]]s, along with the two operations of [[addition]] and [[multiplication]], form the prototypical example of a ring.](https://commons.wikimedia.org/wiki/Special:FilePath/Number-line.svg?width=200 "The [[integer]]s, along with the two operations of [[addition]] and [[multiplication]], form the prototypical example of a ring.")
ALGEBRAIC STRUCTURE IN MATHEMATICS, NOT NECESSARILY WITH MULTIPLICATIVE IDENTITY
Ring (algebra); Associative rings; Unit ring; Ring with a unit; Unital ring; Associative ring; Unitary ring; Ring (abstract algebra); Ring with unity; Ring with identity; Ring unit; Ring (math); Ring (maths); Ring mathematics; Ring maths; Ring math; Mathematical ring; Algebraic ring; Arithmetic properties; Ring with Unity; Unitary algebra; Ring axioms; Ring object; Ring of functions
In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. In other words, a ring is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers.
Quotient ring
CONSTRUCTION IN ABSTRACT ALGEBRA
Factor ring; Residue class ring; Residue ring; Quotient Ring; Factor Ring; Quotient associative algebra
In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite similar to the quotient group in group theory and to the quotient space in linear algebra. It is a specific example of a quotient, as viewed from the general setting of universal algebra.
Ring languages
BRANCH OF THE NARROW GRASSFIELDS LANGUAGES; BEST KNOWN MEMBER IS KOM; NAMED AFTER THE OLD RING ROAD OF CENTRAL CAMEROON
Ring language
The Ring or Ring Road languages, spoken in the Western Grassfields of Cameroon, form a branch of the Narrow Grassfields languages. The best-known Ring language is Kom.
Википедия
Unique factorization domain
In mathematics, a unique factorization domain (UFD) (also sometimes called a factorial ring following the terminology of Bourbaki) is a ring in which a statement analogous to the fundamental theorem of arithmetic holds. Specifically, a UFD is an integral domain (a nontrivial commutative ring in which the product of any two non-zero elements is non-zero) in which every non-zero non-unit element can be written as a product of prime elements (or irreducible elements), uniquely up to order and units.
Important examples of UFDs are the integers and polynomial rings in one or more variables with coefficients coming from the integers or from a field.
Unique factorization domains appear in the following chain of class inclusions:
- rngs ⊃ rings ⊃ commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ GCD domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃ algebraically closed fields
