In mathematics, in particular commutative algebra, the concept of fractional ideal is introduced in the context of integral domains and is particularly fruitful in the study of Dedekind domains. In some sense, fractional ideals of an integral domain are like ideals where denominators are allowed. In contexts where fractional ideals and ordinary ring ideals are both under discussion, the latter are sometimes termed integral ideals for clarity.
Read more about Fractional Ideal: Definition and Basic Results, Dedekind Domains, Divisorial Ideal
Famous quotes containing the words fractional and/or ideal:
“Hummingbird
stay for a fractional sharp
sweetness, and’s gone, can’t take
more than that.”
—Denise Levertov (b. 1923)
“As to the family, I have never understood how that fits in with the other ideals—or, indeed, why it should be an ideal at all. A group of closely related persons living under one roof; it is a convenience, often a necessity, sometimes a pleasure, sometimes the reverse; but who first exalted it as admirable, an almost religious ideal?”
—Rose Macaulay (1881–1958)