Nil ideal information

two-sided ideal of a ring is said to be a nil ideal if each of its elements is nilpotent. The nilradical of a commutative ring is an example of a nil ideal; in...

Look up NIL, Nil, or nil in Wiktionary, the free dictionary. Nil often refers to the number zero. Nil or NIL may also refer to: NIL (programming language)...

a nilpotent ideal, and in some classes of rings, the two notions coincide. If an ideal is nilpotent, it is of course nil, but a nil ideal need not be...

radical of an ideal. The sum of the nil ideals of a ring R is the upper nilradical Nil*R or Köthe radical and is the unique largest nil ideal of R. Köthe's...

addition. nil 1.  A nil ideal is an ideal consisting of nilpotent elements. 2.  The (Baer) upper nil radical is the sum of all nil ideals. 3.  The (Baer)...

first order term. Idempotent element (ring theory) Unipotent Reduced ring Nil ideal Nilpotent matrix Polcino Milies & Sehgal (2002), An Introduction to Group...

as the ideal generated by all nil ideals of the ring, which is itself a nil ideal. The set of all nilpotent elements itself need not be an ideal (or even...

Köthe conjecture: if a ring has no nil ideal other than { 0 } {\displaystyle \{0\}} , then it has no nil one-sided ideal other than { 0 } {\displaystyle...

The Kurosh problem on group algebras concerns the augmentation ideal I. If I is a nil ideal, is the group algebra locally nilpotent? There is an important...

elements except for 0. J(R) contains every nil ideal of R. If R is left or right Artinian, then J(R) is a nilpotent ideal. This can actually be made stronger:...

is a nil ideal and every right ideal of R which is not contained in J(R) contains a nonzero idempotent. Replacing "right ideal" with "left ideal" yields...

In 2018 French director Nils Tavernier released the feature film L'incroyable histoire du facteur Cheval (English: The Ideal Palace) about Cheval's life...

interval (2,3). She also found an example of a nil ideal of a ring R that does not lift to a nil ideal of the polynomial ring R[X], disproving a conjecture...

Lie algebra is a nilpotent ideal, which is as large as possible. The nilradical n i l ( g ) {\displaystyle {\mathfrak {nil}}({\mathfrak {g}})} of a finite-dimensional...

Nilus of Sora (also Nil Sorsky or Nil Sorski; Russian: Нил Сорский; secular name: Nikolai Maikov; Russian: Николай Майков; c. 1433 – 7 May 1508) was a...

chemistry, an ideal solution or ideal mixture is a solution that exhibits thermodynamic properties analogous to those of a mixture of ideal gases. The enthalpy...

consideration. Consequently, processes in ideal MHD that convert magnetic energy into kinetic energy, referred to as ideal processes, cannot generate heat and...

and likeness (NIL) deal with Panini America, a trading card company owned by Panini Group. On February 14, Sayin signed another NIL deal this time with...

element of the algebra is nilpotent is called a nil algebra. Nilpotent algebras are trivially nil, whereas nil algebras may not be nilpotent, as each element...

intersection of all prime ideals is zero. This ideal { 0 } {\displaystyle {\sqrt {\{0\}}}} is also denoted by N i l ∗ ( R ) {\displaystyle Nil_{*}(R)\,} and also...

especially sexual assault. Nils Christie, a Norwegian criminology professor, has been theorizing about the concept of the ideal victim since the 1980s. In...