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| | Obesity is the condition in which the body mass index surpasses the general amount. Usually people with BMI exceeding 30 are considered obese. There are certain weight details that one need to be aware of.<br><br>Secondly, you need to consider the build of your body. While all women would like to be considered delicate small flowers, the truth is the fact that ladies come inside all shapes plus sizes, plus a good fat chart can have separate fat ranges for small, medium, plus larger framed ladies.<br><br>Some folks think that it is wise to test plus shed a limited pounds before computing for their body mass index. You have to remember which doing this type of thing is similar to cheating throughout an exam at school. You should measure the real weight in order to receive a clear picture of how harmful we actually are. If you try to get rid of fat before the computation, you could receive a lower body mass index that may effectively mask a real condition. This will create you think which we don't need to go to the doctor or that you don't want to lose weight at all.<br><br>First, we want to determine an BMI for a child. What is a BMI? BMI stands for body mass index that is a amount which takes into account your child's height-to-weight ratio. There is a very complex formula for calculating BMI, but this will be performed instantly and conveniently at a variety of online sites that provide a [http://safedietplansforwomen.com/bmi-calculator bmi calculator men]. You simply plug in a child's fat and height and the program usually calculate your child's BMI. Finding a bmi calculator can be because easy because doing a Google search for that phrase.<br><br>How do we know should you child is really overweight or obese? You physician could assist you determine whether a child meets the criteria for medical weight, though you may be capable to determine at house whether a child meets the criteria for being greatly overweight or obese..<br><br>To observe both videos below takes regarding 90 minutes. Here are the highlights of it. It shows 6 persons inside their home cities with diabetes going to Dr. Cousen's center. One older guy had his blood sugar brought right down to general but left following 2 week because the diet was too difficult to follow. You are able to eat as much because you need yet it is very nonetheless difficult for people to follow.<br><br>Women should usually rely on a Body mass index calculator before they start a fat reduction program. This will furthermore aid ladies understand when they require medical aid for alarming BMI fluctuations or a truly significant / low BMI. Although it is actually possible to calculate the BMI manually with all the help of several formulae and charts, it is actually furthermore greater should you depend on calculator to learn what the ideal BMI is for women of your height. |
| '''Field theory''' is a branch of [[mathematics]] which studies the properties of [[field (mathematics)|field]]s. A field is a mathematical entity for which addition, subtraction, multiplication and division are [[well-defined]].
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| Please refer to [[Glossary of field theory]] for some basic definitions in field theory.
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| ==History==
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| The concept of ''[[field (mathematics)|field]]'' was used implicitly by [[Niels Henrik Abel]] and [[Évariste Galois]] in their work on the solvability of equations.
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| In 1871, [[Richard Dedekind]], called a set of real or complex numbers which is closed under the four arithmetic operations a "field".
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| In 1881, [[Leopold Kronecker]] defined what he called a "domain of rationality", which is a [[field extension]] of the [[Field of rationals|field of rational numbers]] in modern terms.<ref>{{cite book | title=Galois Theory | volume=106 | series=Pure and Applied Mathematics | first=David A. | last=Cox | edition=2nd | publisher=John Wiley & Sons | year=2012 | isbn=1118218426 | page=348 }}</ref>
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| In 1893, [[Heinrich M. Weber]] gave the first clear definition of an abstract field.
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| In 1910 [[Ernst Steinitz]] published the influential paper ''Algebraische Theorie der Körper'' ([[german language|German]]: Algebraic Theory of Fields). In this paper he axiomatically studied the properties of fields and defined many important field theoretic concepts like [[prime field]], [[perfect field]] and the [[transcendence degree]] of a [[field extension]].
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| Galois, who did not have the term "field" in mind, is honored to be the first mathematician linking [[group theory]] and field theory. [[Galois theory]] is named after him. However it was [[Emil Artin]] who first developed the relationship between groups and fields in great detail during 1928-1942.
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| ==Introduction==
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| [[Field (mathematics)|Field]]s are important objects of study in algebra since they provide a useful generalization of many number systems, such as the [[rational number]]s, [[real number]]s, and [[complex number]]s. In particular, the usual rules of [[associativity]], [[commutativity]] and [[distributivity]] hold. Fields also appear in many other areas of mathematics; see the examples below.
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| When abstract algebra was first being developed, the definition of a field usually did not include commutativity of multiplication, and what we today call a field would have been called either a ''commutative field'' or a ''rational domain''. In contemporary usage, a field is always commutative. A structure which satisfies all the properties of a field except possibly for commutativity, is today called a ''[[division ring]]'' or ''division algebra'' or sometimes a ''skew field''. Also ''non-commutative field'' is still widely used. In [[French (language)|French]], fields are called ''corps'' (literally, ''body''), generally regardless of their commutativity. When necessary, a (commutative) field is called ''corps commutatif'' and a skew field ''corps gauche''. The [[German (language)|German]] word for ''body'' is ''Körper'' and this word is used to denote fields; hence the use of the [[blackboard bold]] <math>\mathbb K</math> to denote a field. <!-- see talk page for why other languages are not included. -->
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| The concept of fields was first (implicitly) used to prove that there is no general formula expressing in terms of radicals the roots of a polynomial with rational coefficients of degree 5 or higher.
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| ==Extensions of a field==
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| An extension of a field ''k'' is just a field ''K'' containing ''k'' as a subfield. One distinguishes between extensions having various qualities. For example, an extension ''K'' of a field ''k'' is called ''algebraic'', if every element of ''K'' is a root of some polynomial with coefficients in ''k''. Otherwise, the extension is called ''transcendental''.
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| The aim of [[Galois theory]] is the study of ''algebraic extensions'' of a field.
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| ==Closures of a field==
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| Given a field ''k'', various kinds of closures of ''k'' may be introduced. For example, the [[algebraically closed field|algebraic closure]], the [[separable closure]], the [[cyclic closure]] et cetera. The idea is always the same: If ''P'' is a property of fields, then a ''P''-closure of ''k'' is a field ''K'' containing ''k'', having property ''P'', and which is minimal in the sense that no proper subfield of ''K'' that contains ''k'' has property ''P''.
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| For example if we take ''P(K)'' to be the property "every nonconstant polynomial ''f'' in ''K''[''t''] has a root in ''K''", then a ''P''-closure of ''k'' is just an [[algebraic closure]] of ''k''.
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| In general, if ''P''-closures exist for some property ''P'' and field ''k'', they are all isomorphic. However, there is in general no preferable isomorphism between two closures.
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| ==Applications of field theory==
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| The concept of a field is of use, for example, in defining [[vector space|vector]]s and [[matrix (mathematics)|matrices]], two structures in [[linear algebra]] whose components can be elements of an arbitrary field.
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| [[Finite field]]s are used in [[number theory]], [[Galois theory]] and [[coding theory]], and again algebraic extension is an important tool.
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| [[Binary field]]s, fields of [[characteristic (algebra)|characteristic]] 2, are useful in [[computer science]].
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| == Some useful theorems ==
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| *[[Isomorphism extension theorem]]
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| *[[Rational variety#Classical results|Lüroth's theorem]]
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| *[[Primitive element theorem]]
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| *[[Wedderburn's little theorem]]
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| ==See also==
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| * [[ring (mathematics)|Ring]]
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| * [[Vector space]]
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| * [[Category of fields]]
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| ==References==
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| {{reflist}}
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| * {{cite book | first=R.B.J.T. | last=Allenby | title=Rings, Fields and Groups|publisher= Butterworth-Heinemann | year=1991 | id=ISBN 0-340-54440-6}}
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| * {{cite book | first1=T.S. | last1=Blyth | first2=E.F. | last2=Robertson | title=Groups, rings and fields: Algebra through practice, Book 3| publisher= Cambridge University Press| year=1985| id=ISBN 0-521-27288-2}}
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| * {{cite book | first1=T.S. | last1=Blyth | first2=E.F. | last2=Robertson | title=Rings, fields and modules: Algebra through practice, Book 6| publisher= Cambridge University Press| year=1985| id=ISBN 0-521-27291-2}}
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| [[Category:Field theory| ]]
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Obesity is the condition in which the body mass index surpasses the general amount. Usually people with BMI exceeding 30 are considered obese. There are certain weight details that one need to be aware of.
Secondly, you need to consider the build of your body. While all women would like to be considered delicate small flowers, the truth is the fact that ladies come inside all shapes plus sizes, plus a good fat chart can have separate fat ranges for small, medium, plus larger framed ladies.
Some folks think that it is wise to test plus shed a limited pounds before computing for their body mass index. You have to remember which doing this type of thing is similar to cheating throughout an exam at school. You should measure the real weight in order to receive a clear picture of how harmful we actually are. If you try to get rid of fat before the computation, you could receive a lower body mass index that may effectively mask a real condition. This will create you think which we don't need to go to the doctor or that you don't want to lose weight at all.
First, we want to determine an BMI for a child. What is a BMI? BMI stands for body mass index that is a amount which takes into account your child's height-to-weight ratio. There is a very complex formula for calculating BMI, but this will be performed instantly and conveniently at a variety of online sites that provide a bmi calculator men. You simply plug in a child's fat and height and the program usually calculate your child's BMI. Finding a bmi calculator can be because easy because doing a Google search for that phrase.
How do we know should you child is really overweight or obese? You physician could assist you determine whether a child meets the criteria for medical weight, though you may be capable to determine at house whether a child meets the criteria for being greatly overweight or obese..
To observe both videos below takes regarding 90 minutes. Here are the highlights of it. It shows 6 persons inside their home cities with diabetes going to Dr. Cousen's center. One older guy had his blood sugar brought right down to general but left following 2 week because the diet was too difficult to follow. You are able to eat as much because you need yet it is very nonetheless difficult for people to follow.
Women should usually rely on a Body mass index calculator before they start a fat reduction program. This will furthermore aid ladies understand when they require medical aid for alarming BMI fluctuations or a truly significant / low BMI. Although it is actually possible to calculate the BMI manually with all the help of several formulae and charts, it is actually furthermore greater should you depend on calculator to learn what the ideal BMI is for women of your height.