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...
37 KB (6,347 words) - 13:52, 10 September 2024
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...
7 KB (1,095 words) - 22:00, 9 May 2024
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...
13 KB (1,766 words) - 09:56, 30 January 2024
In algebra, ring theory is the study of rings, algebraic structures in which addition and multiplication are defined and have similar properties to those...
24 KB (3,093 words) - 04:03, 3 October 2024
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...
9 KB (1,488 words) - 12:03, 26 November 2023
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...
14 KB (2,148 words) - 19:44, 15 September 2024
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...
17 KB (2,956 words) - 00:21, 24 September 2024
fractional ideals of an integral domain are like ideals where denominators are allowed. In contexts where fractional ideals and ordinary ring ideals are both...
10 KB (1,605 words) - 19:27, 23 August 2024
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...
40 KB (5,798 words) - 13:01, 5 July 2024
mathematics, specifically ring theory, a left primitive ideal is the annihilator of a (nonzero) simple left module. A right primitive ideal is defined similarly...
3 KB (287 words) - 19:00, 12 August 2023