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In mathematics an ideal number is an algebraic integer which represents an ideal in the ring of integers of a number field; the idea was developed by Kummer, and led to Dedekind 's ... http://en.wikipedia.org/wiki/Ideal_number
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A type of number involving the roots of unity which was developed by Kummer while trying to solve Fermat's last theorem. Although factorization over the integers is unique (the ... http://mathworld.wolfram.com/IdealNumber.html
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In mathematics, the extent to which unique factorization fails in the ring of integers of an algebraic number field (or more generally any Dedekind domain) can be described by a ... http://en.wikipedia.org/wiki/Class_number_%28number_theory%29
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These ?ideal numbers? were in fact ideals, and in Dedekind domains, unique factorization of ideals does indeed hold. The term ?ideal number? is no longer used; the term ... http://planetmath.org/?op=getobj&from=objects&name=Ideal
... and, in a sense, the class number is a measure of the failure of unique factorization in the original number ring. In 1871, Dedekind showed that every nonzero ideal in the domain ... http://mathworld.wolfram.com/Ideal.html
In Macaulay2, each ideal comes equipped with a matrix of generators. It is the number of columns of this matrix which is returned. If the ideal is homogeneous, this may or may ... http://www.math.uiuc.edu/Macaulay2/doc/Macaulay2-1.1/share/doc/Macaulay2/Macaulay2Doc/html/_numgens_lp__Ideal_rp.html
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basis (self) Return an immutable sequence of elements of this ideal (note: their parent is the number field) that form a basis for this ideal viewed as a ZZ-module. source code http://sage.math.washington.edu/home/mhansen/sage-epydoc/sage.rings.number_field.number_field_ideal.NumberFieldIdeal-class.html
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... constant = 8.3145 J/mol K N = number of molecules k = Boltzmann constant = 1.38066 x 10-23 J/K = 8.617385 x 10-5 eV/K k = R/N A; N A = Avogadro's number = 6.0221 x 10 23 /mol The ideal gas ... http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idegas.html
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