Rings whose nonzero modules have maximal submodules
AA Tuganbaev - Journal of Mathematical Sciences, 2002 - Springer
All rings are assumed to be associative and (except for nil-rings and some stipulated cases)
to have nonzero identity elements. Expressions such as a “Noetherian ring” mean that the …
to have nonzero identity elements. Expressions such as a “Noetherian ring” mean that the …
Maximal submodules and locally perfect rings
AA Tuganbaev - Mathematical Notes, 1998 - Springer
Rings over which every nonzero right module has a maximal submodule are called right
Bass rings. For a ring A module-finite over its center C, the equivalence of the following …
Bass rings. For a ring A module-finite over its center C, the equivalence of the following …
Rings over which each module possesses a maximal submodule
AA Tuganbaev - Mathematical Notes, 1997 - Springer
Right Bass rings are investigated, that is, rings over which any nonzero right module has a
maximal submodule. In particular, it is proved that if any prime quotient ring of a ring A is …
maximal submodule. In particular, it is proved that if any prime quotient ring of a ring A is …
[引用][C] Rings with the minimum condition for principal right ideals have the maximum condition for principal left ideals
D Jonah - Mathematische Zeitschrift, 1970 - Springer
A ring R is said to have the ascending chain condition on cyclic left modules if each
ascending chain of cyclic submodules of a module terminates. If a ring R has this property …
ascending chain of cyclic submodules of a module terminates. If a ring R has this property …
Rings all of whose finitely generated modules are injective.
BL Osofsky - 1964 - msp.org
Proof. For any ring R with identity, it is easy to see that a right ideal/of R is generated by an
idempotent if and only if/is a direct summand of the right iϋ-module RR. If I is an injective …
idempotent if and only if/is a direct summand of the right iϋ-module RR. If I is an injective …
Rings in which minimal left ideals are projective
R Gordon - Pacific Journal of Mathematics, 1969 - msp.org
Let R be an associative ring with identity. Then the left socle of R is a direct summand of R
as a right R-module if and only if it is projective as a left R-module and contains no infinite …
as a right R-module if and only if it is projective as a left R-module and contains no infinite …
Idealizers and nonsingular rings
K Goodearl - Pacific Journal of Mathematics, 1973 - msp.org
This paper deals with the relationship between a ring T and the idealizer R of a right ideal M
of T.[The ring R is the largest subring of T which contains M as a two-sided ideal.] Assuming …
of T.[The ring R is the largest subring of T which contains M as a two-sided ideal.] Assuming …
[PDF][PDF] Finite rings with exactly two maximal subrings
SS Korobkov - Russian Mathematics, 2011 - researchgate.net
In this paper we study two types of finite associative rings, namely, rings with only one
maximal subring and those with exactly two maximal subrings. It is easy to see that the …
maximal subring and those with exactly two maximal subrings. It is easy to see that the …
Rings over which every module has a maximal submodule
LA Koifman - Mathematical notes of the Academy of Sciences of the …, 1970 - Springer
Rings over which every module has a maximal submodule Page 1 RINGS OVER WHICtt
EVERY MODULE HAS A MAXIMAL SUBMODULE LA Koifman UDC 512.4 We consider Bass's …
EVERY MODULE HAS A MAXIMAL SUBMODULE LA Koifman UDC 512.4 We consider Bass's …
Rings whose modules have maximal submodules
C Faith - Publicacions matematiques, 1995 - JSTOR
A ring R is a right max ring if every right module M≠ 0 has at least one maximal submodule.
It suffices to check for maximal submodules of a single module and its submodules in order …
It suffices to check for maximal submodules of a single module and its submodules in order …