- and
ascending chain condition in
modules over
semiprimary rings. A ring R (with 1) is
called semiprimary if R/J(R) is
semisimple and J(R) is a nilpotent...
- The
endomorphism ring of a
module with
finite composition length is a
semiprimary ring. The
endomorphism ring of a
continuous module or
discrete module...
- (semi-)hereditary
right (or left)
nonsingular right (or left)
coherent semiprimary,
right (or left) perfect,
semiperfect semilocal Examples of properties...
- R-module
contains a
minimal submodule.
Right or left
Artinian rings, and
semiprimary rings are
known to be right-and-left perfect. The
following is an example...
- (1) R/J(R) is
semisimple and (2)
idempotents lift
modulo J(R).
semiprimary A
semiprimary ring is a ring R such that, for the
Jacobson radical J(R) of R...
- definition. Left or
right Artinian rings, left or
right perfect rings,
semiprimary rings and von
Neumann regular rings are all
examples of ****ociative Zorn...
-
Artinian and
Noetherian conditions are
equivalent for
modules over a
semiprimary ring.
Noetherian module Ascending/Descending
chain condition Composition...
- 109), Lam (1999, §§8C,19B),
Nicholson &
Yousif (2003, p.51). Let R be a
semiprimary ring with
Jacobson radical J. If R is commutative, or if R/J is a simple...
