-injective) if
Left 𝑊𝑀𝐶2 Rings
... L be any proper essential left ideal of R and f : L → N any nonzero left R−homomorphism. Then L/U ∼ N, where U ker f is a maximal submodule of L. Now L U ⊕ V , where V ∼ N R1 − e is a minimal left ideal of R. Since e is ...
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On Slightly Compressible-Injective Modules
... principally injective modules for commutative rings in ...principally injective (or p-injective), if every R- homomorphism from a principal right ideal of R to M can be extended to one from ...
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Principally Quasi-Injective Semimodules
... Definition 4 (7). An ℛ-semimodule ℬ is called P- injective if for any principal ideal Ų of ℛ and each ℛ-homomorphism f: Ų ℬ, there exists an ℛ- homomorphism g: ℛ ℬ, which extends f. Example 5. ℚ as a ℤ ...
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Vol 3, No 3 (2012)
... principally injective (briefly, small PM − principally injective) if, every R − monomorphism from an M − cyclic small submodule of M to N can be extended to an R − homomorphism from M to N ...
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Graded Essential Extensions and Graded Injective Modules
... ∈ I , or equivalently, if for any x ∈ N the homogenous components of x are again in N. By N ≤ gr M we denote a graded submodule N of the graded module M. If M ∈ − R gr and K ≤ gr M then by Zorn's lemma there exist a ...
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S Injective Modules and Rings
... In this paper we introduce and investigate the notion of 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 ...
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Some Notes on Semiabelian Rings
... we have eR1 − e 0. Since R is idempotent reversible, 1 − eRe 0. So e is central. Now let L be any proper essential left ideal of R and f : L → N any non-zero left R-homomorphism. Then L/U ∼ N, where U kerf is a maximal ...
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Some Remarks on Finitely Quasi-injective Modules
... MGP- injective [ 11 ] if, for any 0 6= a ∈ R, there exists a positive integer n such that a n 6= 0 and any R-monomorphism from a n R to R extends to an endomorphism of R; a ring R is said to be right ...
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Rings which have \((m, n)\)-flat injective modules
... over G. An R-module M is said to be n-generated if it has a generating set of cardinality at most n[6]. A left R-module M is called (m, n)- injective if for every n-generated submodule K of the left R-module R m , ...
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Rad-supplements in injective modules
... almost injective module is ...almost injective. Then we investigate the structure of Rad-s-injective modules over some type of ...is injective. Another characterization of ...
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About the Closed Quasi Injective S-Acts Over Monoids
... C-quasi injective is C-quasi injective if they are fully invariant, while, proposition ...C-M- injective and the converse is true also, this means if the product is C-M-injective, then each M ...
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Sigma-pure-injective modules for string algebras and linear relations
... It is well-known that the finite-dimensional indecomposable modules for a string algebra are classified in terms of strings and bands, see for example [3, 4]. It is also interesting to study infinite-dimensional modules, ...
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On χ-injective modules
... Definition 3.1. Let M be a right R module and χ be a collection of right ideals of R. Then M is said to be χ-injective if every homomorphism f : I → M, I ∈ χ can be extended to whole of R. Example 3.1.Let M be a ...
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AGQP Injective Modules
... 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 Ra for all a ∈ ...
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On injective L modules
... modules, injective modules, and the like form an important area in module ...for injective L-modules and prove that a direct sum of L-modules is injective if and only if each L-module in the sum is ...
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Vol 8, No 1 (2017)
... Equivalently, l r (a) M R = Ma for all a ∈ R where l and r are left and right annihilators, respectively. This notion was introduced by Camillo [2] for commutative rings. In [8], Nicholson and Yousif studied the ...
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Exact sequences of graphs
... Let Γ and Υ be graphs. A function φ : V (Γ) → V (Υ) is a homomor- phism from Γ to Υ if it preserves edges, that is, if for any edge [x, x ′ ] of Γ, [φ(x), φ(x ′ )] is an edge of Υ. A homomorphism φ : Γ → Υ is called f ...
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A Module Whose Second Spectrum Has the Surjective or Injective Natural Map
... A submodule N of M is said to be cocyclic if N ⊆ E(R/m) for some maximal ideal m of R (here E(R/m) denote the injective envelope of R/m) (see [29]). The cosupport of M , denoted by Cosupp(M ), is defined as the ...
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REEDY CATEGORIES AND THEIR GENERALIZATIONS MICHAEL SHULMAN
... Recall that the category Cat has a canonical model structure, in which the weak equivalences are the equivalences of categories and the cofibrations are the functors that are injective o[r] ...
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Anti-diabetic medication pattern in Adama Hospital Medical College East Shoa Zone, Oromia, Ethiopia
... combination. Injective anti-diabetic drug monotherapy was the predominant treatment for DM and oral anti-diabetic drugs combination was the predominant in this ...
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