[PDF] Top 20 Rings which have \((m, n)\)-flat injective modules

... R-module N is called T-finitely generated (resp. H-finitely generated) if N contains a finitely generated submodule N 0 such that N/N 0 ⊗ R ∗ = ... See full document

... hyperrings which was introduced by Davvaz and Vougiouklis in [9] (for more details see ...(m, n)-hyperrings, in framework of mul- tialgebras theory and universial ...(m, n)-hyperrings, ... See full document

... each m-presented module is n-presented for m ≥ ...right n-coherent in case every n-presented right R-module is n ...every n-coherent ring is m-coherent for m ... See full document

... on rings and modules can be found in [2]. Finally, if N is a submodule of an R-module M, then for any x ∈ M, (N : x) will denote the right ideal of R given by { a ∈ R | xa ∈ ... See full document

... s-injective Modules and Rings. A right R-module M is called right s-N-injective, where N is a right R-module, if every R-homomorphism f K : → M extends to N ... See full document

... R m (Ann(M )) and qM 6= M . It is enough to show that qM ∈ M ax(M ...Let N be a submodule of M such that qM ⊆ N ⊂ M ...: M = N : M = q. ... See full document

... of M generated by x, in general 〈 〉 *∑ ∑ + and if M is unitary, then 〈 〉 *∑ + ...Let M and N two modules , A mapping is called homomorphism of modules (or homomorphism) if ( ) ( ... See full document

... module M is injective if and only if it is a direct summand of every extension N ...Here N is an extension of M provided M ⊆ N ...[12] injective modules to ... See full document

... ideal m admitting a non-zero element a ∈ m for which the ideal (0 : a) is isomorphic to ...R-modules M , with particular attention to the case when m 4 = ...of m . If R is ... See full document

... module M R is called finitely quasi-injective (or FQ-injective for short) [ 7 ] if each R-homomorphism from a finitely generated submodule of M to M can be extended to an endomorphism ... See full document

... principally injective modules for commutative rings in ...R-module M is called principally injective (or p-injective), if every R- homomorphism from a principal right ideal of R ... See full document

... all rings are associative with an identity ...all modules are unital left R-modules. Let M be a ...use N 6 M to denote that N is a submodule M ...of M and ... See full document

... and injective modules constitutes the backbone of the modern homological ...algebra. Injective modules are closely related to essential ...R-module M is injective if and only if ... See full document

... differential rings constructed from quasiprime ideals via quotient rings and rings of fractions were studied ...ideal M such that I M ... See full document

... all modules are ...principally injective 1 or right P-injective for short if, every homomorphism from a principal right ideal of R to R can be extended to an endomorphism of R, or equivalently, lra ... See full document

... (a) M R = Ma for all a ∈ R where l and r are left and right annihilators, ...principally injective rings and gave some ...principally injective rings to the one for ...-injective ... See full document

... endomorphism rings of quasiprincipally injective modules and on maximal right ideals of right AP-injective rings to maximal left ideals of the endomorphism rings of ... See full document

... is n-flat (resp., weakly n-flat) if and only if R is an (n,n − 1)-ring ...of n-von Neumann regular rings and a characterization of weak n-von Neumann regular ... See full document

... Let M and N be R-modules and let µ ∈ L(M) and ν ∈ ...of M onto N is called a weak isomorphism of µ into ν if f (µ) ⊆ ν ... See full document

... et M be a right R − module. A right R − module N is called small pseudo M − principally injective (briefly, small PM − principally injective) if, every R − monomorphism from an M ... See full document