- In mathematics, the
adjective Noetherian is used to
describe objects that
satisfy an
ascending or
descending chain condition on
certain kinds of subobjects...
- 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...
- 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...
- In
abstract algebra, a
Noetherian module is a
module that
satisfies the
ascending chain condition on its submodules,
where the
submodules are partially...
-
Noetherian and Artinian.
Homomorphic images and
subgroups of
Noetherian groups are
Noetherian, and an
extension of a
Noetherian group by a
Noetherian...
-
chains of
prime ideals. The
Krull dimension need not be
finite even for a
Noetherian ring. More
generally the
Krull dimension can be
defined for
modules over...
- In
commutative algebra, a quasi-excellent ring is a
Noetherian commutative ring that
behaves well with
respect to the
operation of completion, and is called...
-
rings over a
field are
Noetherian is
called Hilbert's
basis theorem. Moreover, many ring
constructions preserve the
Noetherian property. In particular...
- a
semiprimary ring and M is an R-module, the
three module conditions Noetherian,
Artinian and "has a
composition series" are equivalent.
Without the semiprimary...
- In mathematics, a
Noetherian topological space,
named for Emmy Noether, is a
topological space in
which closed subsets satisfy the
descending chain condition...
