ring theory, a branch of mathematics, a radical of a ring is an ideal of "not-good"[definition needed] elements of the ring. The first example of a radical...
13 KB (1,742 words) - 14:11, 1 April 2025
mathematics, more specifically ring theory, the Jacobson radical of a ring R {\displaystyle R} is the ideal consisting of those elements in R {\displaystyle...
26 KB (2,891 words) - 21:16, 3 June 2025
thus the radical of the zero ideal. If the nilradical is the zero ideal, the ring is called a reduced ring. The nilradical of a commutative ring is the...
7 KB (1,066 words) - 10:27, 20 February 2025
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...
12 KB (2,131 words) - 09:53, 19 November 2024
more specifically in ring theory, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the integers, such as...
38 KB (6,311 words) - 06:06, 29 June 2025
Radical of an ideal, an important concept in abstract algebra Radical of a ring, an ideal of "bad" elements of a ring Jacobson radical, consisting of...
4 KB (561 words) - 15:03, 22 May 2025
Quasiregular element (category Ring theory)
specifically ring theory, the notion of quasiregularity provides a computationally convenient way to work with the Jacobson radical of a ring. In this article...
12 KB (1,658 words) - 09:31, 14 March 2025
Affine variety (redirect from Ring of regular functions)
ring in one indeterminate) is called the coordinate ring of X. The ideal I ( X ) {\displaystyle \mathrm {I} (X)} is radical, so the coordinate ring is...
31 KB (4,377 words) - 22:02, 13 June 2025
Nakayama's lemma (category Theorems in ring theory)
the Jacobson radical of a ring (typically a commutative ring) and its finitely generated modules. Informally, the lemma immediately gives a precise sense...
22 KB (3,604 words) - 05:48, 21 November 2024
In mathematics, a ring is an algebraic structure consisting of a set with two binary operations called addition and multiplication, which obey the same...
99 KB (13,697 words) - 09:39, 16 June 2025
Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This...
32 KB (4,255 words) - 02:03, 6 May 2025
Retrieved 2013-10-14. "Pagani Zonda breaks 'Ring record". Evo. 13 November 2018. Retrieved 2024-05-13. "2007 Radical SR8LM - Images, Specifications and Information"...
4 KB (159 words) - 17:31, 6 March 2025
Local rings also do not have such idempotents, but for a different reason. The only idempotent contained in the Jacobson radical of a ring is 0. A ring in...
19 KB (2,329 words) - 16:20, 26 June 2025
integers. Ring theory studies the structure of rings; their representations, or, in different language, modules; special classes of rings (group rings, division...
24 KB (3,093 words) - 19:58, 15 June 2025
Karl Ziegler (category Werner von Siemens Ring laureates)
involving free-radicals, many-membered rings, and organometallic compounds, as well as the development of Ziegler–Natta catalyst. One of many awards Ziegler...
23 KB (2,670 words) - 09:37, 15 March 2025
criterion on normality) radical 1. The Jacobson radical of a ring. 2. The nilradical of a ring. 3. A radical of an element x of a ring is an element such...
66 KB (9,772 words) - 22:19, 27 May 2025
theory of modules, the radical of a module is a component in the theory of structure and classification. It is a generalization of the Jacobson radical for...
2 KB (324 words) - 06:52, 7 July 2025
rings are the most common products; formation of smaller and larger rings is rarely observed. Three conditions must be met for an efficient radical cyclization...
15 KB (1,902 words) - 18:07, 27 May 2025
radicals highly chemically reactive. Many radicals spontaneously dimerize. Most organic radicals have short lifetimes. A notable example of a radical...
41 KB (4,607 words) - 22:34, 15 June 2025
algebra, a semiprimitive ring or Jacobson semisimple ring or J-semisimple ring is a ring whose Jacobson radical is zero. This is a type of ring more general...
3 KB (372 words) - 18:27, 14 June 2022
algebra, a Hilbert ring or a Jacobson ring is a ring such that every prime ideal is an intersection of primitive ideals. For commutative rings primitive...
6 KB (836 words) - 14:45, 10 November 2024
Semisimple module (redirect from Semisimple ring)
Jacobson radical is zero. If an Artinian semisimple ring contains a field as a central subring, it is called a semisimple algebra. For a commutative ring, the...
10 KB (1,249 words) - 15:50, 18 September 2024
Nil ideal (category Ideals (ring theory))
radical of a ring. Because the nil radical contains every nilpotent element, an ideal of a commutative ring is nil if and only if it is a subset of the nil...
5 KB (734 words) - 22:17, 1 June 2025
ideal and with the ring's Jacobson radical. The third of the properties listed above says that the set of non-units in a local ring forms a (proper) ideal...
15 KB (2,300 words) - 20:46, 1 June 2025
unnecessary. A semiprimitive ring or Jacobson semisimple ring or J-semisimple ring is a ring whose Jacobson radical is zero. This is a type of ring more general...
20 KB (2,804 words) - 01:41, 1 November 2023
Phenyl group (redirect from Phenyl radical)
In organic chemistry, the phenyl group, or phenyl ring, is a cyclic group of atoms with the formula C6H5, and is often represented by the symbol Ph (archaically...
9 KB (1,048 words) - 21:01, 1 June 2025
radical of an ideal I in a polynomial ring with real coefficients is the largest ideal containing I with the same (real) vanishing locus. It plays a similar...
2 KB (327 words) - 01:56, 28 April 2024
a radical clock is a chemical compound that assists in the indirect methodology to determine the kinetics of a free-radical reaction. The radical-clock...
8 KB (1,004 words) - 16:56, 9 November 2023
Nilpotent ideal (category Ideals (ring theory))
that any nil ideal is contained in the Jacobson radical of the ring, and since the Jacobson radical is a nilpotent ideal (due to the Artinian hypothesis)...
3 KB (357 words) - 07:01, 1 September 2023
aryl radical in organic chemistry is a reactive intermediate and an arene compound incorporating one free radical carbon atom as part of the ring structure...
2 KB (222 words) - 19:37, 27 October 2022