mathematics, and more specifically in ring theory, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the integers...

mathematics, ideal theory is the theory of ideals in commutative rings. While the notion of an ideal exists also for non-commutative rings, a much more...

theory, an ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion of a ring ideal of...

In algebra, ring theory is the study of rings, algebraic structures in which addition and multiplication are defined and have similar properties to those...

more specifically in ring theory, a maximal ideal is an ideal that is maximal (with respect to set inclusion) amongst all proper ideals. In other words, I...

ideal class group (or class group) of an algebraic number field K is the quotient group JK /PK where JK is the group of fractional ideals of the ring...

In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite...

fractional ideals of an integral domain are like ideals where denominators are allowed. In contexts where fractional ideals and ordinary ring ideals are both...

an ideal, fundamental to ring theory. (The word "Ring", introduced later by Hilbert, does not appear in Dedekind's work.) Dedekind defined an ideal as...

In ring theory, a branch of mathematics, the radical of an ideal I {\displaystyle I} of a commutative ring is another ideal defined by the property that...