Algebraic integer
Algebraic integer In mathematics, an algebraic integer is an algebraic number that is a ... polynomial whose leading coefficient is 1) with integer coefficients. In more abstract terms, the ring ... is a non-monic primitive polynomial with integer coefficients that is irreducible over Q, then ... of two algebraic integers is an algebraic integer, and so is their difference; their ...
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Square-free integer
Square-free integer In mathematics, a square-free, or quadratfrei, integer is one divisible by no perfect square ... Equivalent characterizations of square-free numbers The integer n is square-free if and only ... a and b are coprime. The positive integer n is square-free if and only ... μ denotes the Möbius function. The positive integer n is square-free if and ...
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Radical of an ideal
Radical of an ideal In ring theory, a branch of mathematics, the radical of an ideal is a kind of ... such as the nilradical and the Jacobson radical, which isolate certain "bad" properties of the ring. A radical ideal is an ideal that is its own radical (this can be phrased as being ...
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Talk:Law of excluded middle
... through rigid definitions. There can be no integer between five and six, and the fact ... that the square root of a positive integer must be an integer should it be rational depends upon equality ... 2 cannot have the qualities of an integer and thus must be something other than ... short stature. Such an expression as "the integer between five and six" or "the ...
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Exponentiation
... the axes is one unit. Exponentiation with integer exponents The exponentiation operation with integer exponents only requires basic algebra. Positive integer exponents The simplest case involves a positive integer exponent. The exponent then says how many ... exponentiation by squaring. Formally, powers with positive integer exponents are defined by the initial ...
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Talk:Square root
... time consuming than a multiplication in computer integer arithmetic. The iteration for $g(x\; ...\; of\; "f".\; In\; practical\; implementations\; of\; large$integer square roots, the iteration involving "g" is ... 17th century or so. They denoted a radical with an "r" in front of the ... their pens from the paper, and the radical sign was born. Contrary to popular belief, the use of the radical to represent roots can actually be ...
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Talk:Base (mathematics)
... — are bases ever used for non-integer numbers? Neonumbers 09:55, 25 January 2006 ... caveat that in a particular base, the radical expansion may not terminate (just like 0 ... only do most people not use non integer numbers "in practice"; most people never use ... was intended not to refer to non-integer bases, but non-integer numbers in bases other than ten. ...
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Glossary of ring theory
... is nilpotent if there exists a positive integer n such that r n = 0. Unit ... left ideal and a right ideal. Jacobson radical The intersection of all maximal left ideals ... forms a two-sided ideal, the Jacobson radical of the ring. Kernel of a ring ... not' equal, in general, to the Jacobson Radical. Prime ideal An ideal P in a ... RaR for some element a of R. Radical of an ideal The radical of ...
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IUPAC nomenclature   (translated from Chinese)
... the substituting group, calls the hydrocarbon oxygen radical. Mellow The mellow naming, take includes the ... imines, on the nitrogen atom short alkyl radical regards makes the substituting group, the naming ... When naming, called first the link the integer, then marks on each link in the ... between the bridge head carbon carbon atom integer, between the numeral separates with the spot, digital integer always compared to ring content more ...
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Talk:Function (mathematics)
... of all natural numbers, that pairs each integer x with its square x². Another example ... amazing thing is that in the numerous radical rewrites that I did before, in articles ... lexical comparison, I never ran into such radical differences of taste as I found here ... respectively, but that would have been too radical an innovation, plus transposing the F and ... of all natural numbers, that pairs each integer x with its square x². Another ...
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