In mathematics, specifically abstract algebra, an Artinian ring (sometimes Artin ring) is a ring that satisfies the descending chain condition on ...

Artinian rings, and especially local Artinian rings, play an important role in algebraic geometry, for example in deformation theory.

16 июн. 2021 г. · A ring is called local if it has only one maximal ideal, and it is called semilocal if the number of maximal ideals of the ring is finite.

19 авг. 2024 г. · In an artinian ring R R the Jacobson radical J ( R ) J(R) is nilpotent. A left artinian ring is semiprimitive if and only if the zero ideal is ...

Artinian rings. Definition 0.1. A ring A is Artinian if it satisfies the DCC (Descending Chain. Condition): every descending chain of ideals of A,.

A ring is called left (respectively right) Artinian if it does not contain an infinite descending chain of left (resp. right) ideals. In this case the ring ...

We now want to show that Theorem 5.2 implies that a left artinian ring R with N(R) = 0 is automatically a direct sum of matrix rings over division rings (the ...

28 апр. 2017 г. · The statement you report is not a definition, but a theorem. If R is a commutative Artinian ring with no zero divisors, then R is a field. Example of Artinian ring - Mathematics Stack Exchange Commutative artinian ring is noetherian - Math Stack Exchange does simple ring implies artinian ring? - Math Stack Exchange Spectrum of Artinian ring - Mathematics Stack Exchange Другие результаты с сайта math.stackexchange.com

An Artinian ring is a ring in which every descending chain of ideals eventually stabilizes. This property indicates that the ring has a certain 'finiteness' ...