- In mathematics, a
Noetherian ring is a ring that
satisfies the
ascending chain condition on left and
right ideals; if the
chain condition is satisfied...
- In mathematics, the
adjective Noetherian is used to
describe objects that
satisfy an
ascending or
descending chain condition on
certain kinds of subobjects...
- In
abstract algebra, a
Noetherian module is a
module that
satisfies the
ascending chain condition on its submodules,
where the
submodules are partially...
- In mathematics, a
Noetherian topological space,
named for Emmy Noether, is a
topological space in
which closed subsets satisfy the
descending chain condition...
- is a
Noetherian ring. More generally, a
scheme is
locally Noetherian if it is
covered by
spectra of
Noetherian rings. Thus, a
scheme is
Noetherian if and...
-
Noetherian and Artinian.
Homomorphic images and
subgroups of
Noetherian groups are
Noetherian, and an
extension of a
Noetherian group by a
Noetherian...
-
rings over a
field are
Noetherian is
called Hilbert's
basis theorem. Moreover, many ring
constructions preserve the
Noetherian property. In particular...
-
deduce theorems of
interest for
usual schemes. A
locally Noetherian scheme is a
locally Noetherian formal scheme in the
canonical way: the
formal completion...
-
Since an
Artinian ring is also a
Noetherian ring, and finitely-generated
modules over a
Noetherian ring are
Noetherian, it is true that for an Artinian...
- In mathematics, the Lasker–Noether
theorem states that
every Noetherian ring is a
Lasker ring,
which means that
every ideal can be
decomposed as an intersection...
