plural of left ideal

plural of two-sided ideal

(philosophy) A school of philosophy first proposed by Immanuel Kant. It can be juxtaposed with transcendental realism in that it views things in terms of how they appear to the actor rather than how they actually are.

(physics) a hypothetical gas, whose molecules exhibit no interaction, and undergo elastic collision with each other and with the walls of the container

plural of ideal number

(number theory) An algebraic integer that represents an ideal in the ring of integers of a number field.

(algebra, ring theory) Any (two-sided) ideal I such that for arbitrary ideals P and Q, PQ⊆I⟹P⊆I or Q⊆I.

(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).

(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.

(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).