Definitions for integrality
in·te·gral·i·ty

Princeton's WordNetRate this definition:0.0 / 0 votes

1. entirety, entireness, integrality, totalitynoun

   the state of being total and complete

   "he read the article in its entirety"; "appalled by the totality of the destruction"

WiktionaryRate this definition:0.0 / 0 votes

1. integralitynoun

   The condition of being integral

WikipediaRate this definition:0.0 / 0 votes

1. integrality

   In commutative algebra, an element b of a commutative ring B is said to be integral over A, a subring of B, if there are n ≥ 1 and aj in A such that b n + a n − 1 b n − 1 + ⋯ + a 1 b + a 0 = 0. {\displaystyle b^{n}+a_{n-1}b^{n-1}+\cdots +a_{1}b+a_{0}=0.} That is to say, b is a root of a monic polynomial over A. The set of elements of B that are integral over A is called the integral closure of A in B. It is a subring of B containing A. If every element of B is integral over A, then we say that B is integral over A, or equivalently B is an integral extension of A. If A, B are fields, then the notions of "integral over" and of an "integral extension" are precisely "algebraic over" and "algebraic extensions" in field theory (since the root of any polynomial is the root of a monic polynomial). The case of greatest interest in number theory is that of complex numbers integral over Z (e.g., 2 {\displaystyle {\sqrt {2}}} or 1 + i {\displaystyle 1+i} ); in this context, the integral elements are usually called algebraic integers. The algebraic integers in a finite extension field k of the rationals Q form a subring of k, called the ring of integers of k, a central object of study in algebraic number theory. In this article, the term ring will be understood to mean commutative ring with a multiplicative identity.

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1. integrality

   Integrality generally refers to the state or quality of being whole, complete or undivided, often used in the context of mathematical concepts and functions. It is also used in integer programming in operations research, where variables are required to be integers, and in algebraic number theory to describe algebraic integers.

Webster DictionaryRate this definition:0.0 / 0 votes

1. Integralitynoun

   entireness

2. Etymology: [Cf. F. intgralit.]

How to pronounce integrality?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say integrality in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of integrality in Chaldean Numerology is: 3

2. Pythagorean Numerology

   The numerical value of integrality in Pythagorean Numerology is: 5

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References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=integrality
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Integrality
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Integrality
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Webster Dictionary
   https://www.merriam-webster.com/dictionary/integrality