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...

mathematics, more specifically ring theory, the Jacobson radical of a ring R {\displaystyle R} is the ideal consisting of those elements in R {\displaystyle...

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...

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...

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...

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...

specifically ring theory, the notion of quasiregularity provides a computationally convenient way to work with the Jacobson radical of a ring. In this article...

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...

the Jacobson radical of a ring (typically a commutative ring) and its finitely generated modules. Informally, the lemma immediately gives a precise sense...

Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This...

In mathematics, a ring is an algebraic structure consisting of a set with two binary operations called addition and multiplication, which obey the same...

Retrieved 2013-10-14. "Pagani Zonda breaks 'Ring record". Evo. 13 November 2018. Retrieved 2024-05-13. "2007 Radical SR8LM - Images, Specifications and Information"...

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...

integers. Ring theory studies the structure of rings; their representations, or, in different language, modules; special classes of rings (group rings, division...

involving free-radicals, many-membered rings, and organometallic compounds, as well as the development of Ziegler–Natta catalyst. One of many awards Ziegler...

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...

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...

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...

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...

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...

radicals highly chemically reactive. Many radicals spontaneously dimerize. Most organic radicals have short lifetimes. A notable example of a radical...

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...

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...

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...

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...

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...

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...

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...

theory) Radical of a ring Semiprime ring Nielsen-Schreier theorem O'Connor, John J.; Robertson, Edmund F., "Reinhold Baer", MacTutor History of Mathematics...

semisimple rings are automatically Artinian rings. However, some authors use "semisimple" differently, to mean that the ring has a trivial Jacobson radical. For...