noetherian ring वाक्य
उदाहरण वाक्य
मोबाइल
- Pathological examples found by Nagata led to the reexamination of the roles of Noetherian rings and motivated, among other things, the definition of excellent ring.
- It has a straightforward extension to modules stating that every submodule of a finitely generated module over a Noetherian ring is a finite intersection of primary submodules.
- The integral closure of a Dedekind domain in a finite extension of the field of fractions is a Dedekind domain; in particular, a noetherian ring.
- The Jaffard property is satisfied by any Noetherian ring " R ", so examples of non-Jaffardian rings are quite difficult to find.
- A nonzero finitely generated module " M " over a commutative Noetherian ring is coprimary if and only if it has exactly one associated prime.
- Jean-Pierre Serre defined a regular ring as a commutative noetherian ring of finite global homological dimension and proved that this is equivalent to the definition above.
- The Lasker Noether theorem is an extension of the fundamental theorem of arithmetic, and more generally the fundamental theorem of finitely generated abelian groups to all Noetherian rings.
- He established the concept of the Krull dimension of a ring, first for Noetherian rings before moving on to expand his theory to cover general valuation rings and Krull rings.
- The converse is true for finitely generated modules over Noetherian rings : a finitely generated module over a commutative noetherian ring is locally free if and only if it is projective.
- The converse is true for finitely generated modules over Noetherian rings : a finitely generated module over a commutative noetherian ring is locally free if and only if it is projective.
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