Add to ORKGA module M is said to be modest if the injectivity domain of M is the class of all crumbling modules. In this paper, we investigate the basic properties of modest modules. We provide characterizations of some classes of rings using modest modules. In particular, we show that a ring having the class of crumbling modules as the only right middle class of injectivity domains is either a right V -ring or right Noetherian; and a commutative ring with this property is regular. We also give criteria for a ring having the class of crumbling modules as the only right middle class of injectivity domains
AbstractA module M is said to be weakly injective if every finitely generated submodule of its injec...
International audienceLet R be a ring (not necessarily commutative). A left R-module is said to be c...
International audienceIt is shown that a ring is left semihereditary if and only each homomorphic im...
A module M is said to be modest if the injectivity domain of M is the class of all crumbling modules...
AbstractIn a recent paper, Alahmadi, Alkan and López–Permouth defined a module M to be poor if M is ...
In a recent paper, Alahmadi. Alkan and Lopez-Permouth defined a module M to be poor if M is injectiv...
A poor module is one that is injective relative only to semisimple modules and a module is maximally...
Relative notions of flatness are introduced as a mean to gauge the extent of the flatness of any giv...
Rosenberg and Zelinsky [10] studied rings over which every module of finite length has an injective ...
AbstractGiven modules M and N, M is said to be N-subinjective if for every extension K of N and ever...
A ring R is called a right WV-ring if each simple right R-module is injective relative to proper cyc...
Under study are some conditions for the weakly regular modules to be closed under direct sums and th...
In a recent paper of Alahmadi, Alkan and Lopez-Permouth, a ring R is defined to have no (simple) mid...
AbstractA ring R is called a right weakly V-ring (briefly, a right WV-ring) if every simple right R-...
AbstractLet R be a commutative semilocal ring and U be the minimal injective cogenerator in the cate...
AbstractA module M is said to be weakly injective if every finitely generated submodule of its injec...
International audienceLet R be a ring (not necessarily commutative). A left R-module is said to be c...
International audienceIt is shown that a ring is left semihereditary if and only each homomorphic im...
A module M is said to be modest if the injectivity domain of M is the class of all crumbling modules...
AbstractIn a recent paper, Alahmadi, Alkan and López–Permouth defined a module M to be poor if M is ...
In a recent paper, Alahmadi. Alkan and Lopez-Permouth defined a module M to be poor if M is injectiv...
A poor module is one that is injective relative only to semisimple modules and a module is maximally...
Relative notions of flatness are introduced as a mean to gauge the extent of the flatness of any giv...
Rosenberg and Zelinsky [10] studied rings over which every module of finite length has an injective ...
AbstractGiven modules M and N, M is said to be N-subinjective if for every extension K of N and ever...
A ring R is called a right WV-ring if each simple right R-module is injective relative to proper cyc...
Under study are some conditions for the weakly regular modules to be closed under direct sums and th...
In a recent paper of Alahmadi, Alkan and Lopez-Permouth, a ring R is defined to have no (simple) mid...
AbstractA ring R is called a right weakly V-ring (briefly, a right WV-ring) if every simple right R-...
AbstractLet R be a commutative semilocal ring and U be the minimal injective cogenerator in the cate...
AbstractA module M is said to be weakly injective if every finitely generated submodule of its injec...
International audienceLet R be a ring (not necessarily commutative). A left R-module is said to be c...
International audienceIt is shown that a ring is left semihereditary if and only each homomorphic im...