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ideal gas
(physics) a hypothetical gas, whose molecules exhibit no interaction, and undergo elastic collision with each other and with the walls of the container
beau ideal
Nonstandard spelling of beau idéal.
ideal numbers
plural of ideal number
ideal number
(number theory) An algebraic integer that represents an ideal in the ring of integers of a number field.
prime ideal
(algebra, ring theory) Any (two-sided) ideal I such that for arbitrary ideals P and Q, PQ⊆I⟹P⊆I or Q⊆I.
fractional ideal
(algebra, ring theory) Given an integral domain R and its field of fractions K = Frac(R), an R-submodule I of K such that for some nonzero r∈R, rI ⊆ R.
factor ideal
(algebra, ring theory) For given ring R, any ideal I such that Q = R / I, the set of cosets of elements of I in R, is a ring (the quotient ring of I in R).
maximal ideal
(algebra, ring theory) An ideal which cannot be made any larger (by adjoining any element to it) without making it improper (i.e., equal to the whole of the containing algebraic structure).
primary ideal
(algebra, ring theory) Given a commutative ring R, any ideal I such that for any a,b ∈ R, if ab ∈ I then either b ∈ I or aⁿ ∈ I for some integer n > 0.
