Artinian ring


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Artinian ring

[ar¦tin·ē·ən ′riŋ]
(mathematics)
A ring is Artinian on left ideals (or right ideals) if every descending sequence of left ideals (or right ideals) has only a finite number of distinct members.
References in periodicals archive ?
Suppose A is an artinian ring, with indecomposable A-modules {[P.
Suppose R is an artinian ring that is not semisimple and with two additional indecomposable modules [I.
Every finitely generated module over a right Artinian ring is [pi]-Rickart (see Theorem 2.
Let R be a right Artinian ring and M a finitely generated R-module.
of Wisconsin- Madison) also includes coverage of rarer subjects in this field, including transcendental field extensions, modules over Dedekind domains and artinian rings.