Rad-Projective and Strongly Rad-Projective Modules

Amin, Ismail; Ibrahim, Yasser; Yousif, Mohamed

doi:10.1080/00927872.2012.654552

Cited by 2 publications

(6 citation statements)

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“…That is to say, if Ω is the class of max-projective right R-modules, the homomorphism f : P → M is called max-projective cover of M . With the help of an argument similar to the one provided in [3,Theorem 18], we can establish the next Proposition.…”

Section: Proofmentioning

confidence: 88%

“…A right R-module M is called max-projective provided that each homomorphism f : M → R/I where I is any maximal right ideal, factors through the canonical projection π : R → R/I. This notion properly generalizes the notions R-projective and rad-projective modules studied in [3].…”

Section: Introductionmentioning

confidence: 95%

“…In [3], the module M is called rad-projective if, for any epimorphism σ : R → K where K is an image of R/J(R) and any homomorphism f : M → K, there exists a homomorphism g : M → R such that f = σg. We have the following implications: projective ⇒ R-projective ⇒ rad-projective ⇒ max-projective Proposition 1.…”

Section: Proofmentioning

confidence: 99%

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max-projective modules

Alagöz,

Büyükaşik

2019

Preprint

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A right R-module M is called max-projective provided that each homomorphism f : M → R/I where I is any maximal right ideal, factors through the canonical projection π : R → R/I. We call a ring R right almost-QF (resp. right max-QF ) if every injective right R-module is R-projective (resp. max-projective). This paper attempts to understand the class of right almost-QF (resp. right max-QF ) rings. Among other results, we prove that a right Hereditary right Noetherian ring R is right almost-QF if and only if R is right max-QF if and only if R = S × T , where S is semisimple Artinian and T is right small. A right Hereditary ring is max-QF if and only if every injective simple right R-module is projective. Furthermore, a commutative Noetherian ring R is almost-QF if and only if R is max-QF if and only if R = A × B, where A is QF and B is a small ring.

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Section: Proofmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 95%

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max-projective modules

Alagöz,

Büyükaşik

2019

Preprint

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“…is finitely generated, E/P (E) has finite composition length by Proposition 13 (3). By max-projectivity of E and Lemma 3, E/P (E) is max-projective.…”

Section: -15mentioning

confidence: 91%

“…This notion properly generalizes the notion R-projective modules. This is also a dualization of the notion of mininjective rings and modules that was introduced by Nicholson and Yousif in [27] and a generalization of the work by Amin et al in [3].…”

Section: Introductionmentioning

confidence: 92%

Max-projective modules

Alagöz

Büyükaşık

2020

J. Algebra Appl.

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Weakening the notion of [Formula: see text]-projectivity, a right [Formula: see text]-module [Formula: see text] is called max-projective provided that each homomorphism [Formula: see text], where [Formula: see text] is any maximal right ideal, factors through the canonical projection [Formula: see text]. We study and investigate properties of max-projective modules. Several classes of rings whose injective modules are [Formula: see text]-projective (respectively, max-projective) are characterized. For a commutative Noetherian ring [Formula: see text], we prove that injective modules are [Formula: see text]-projective if and only if [Formula: see text], where [Formula: see text] is [Formula: see text] and [Formula: see text] is a small ring. If [Formula: see text] is right hereditary and right Noetherian then, injective right modules are max-projective if and only if [Formula: see text], where [Formula: see text] is a semisimple Artinian and [Formula: see text] is a right small ring. If [Formula: see text] is right hereditary then, injective right modules are max-projective if and only if each injective simple right module is projective. Over a right perfect ring max-projective modules are projective. We discuss the existence of non-perfect rings whose max-projective right modules are projective.

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Rad-Projective and Strongly Rad-Projective Modules

Cited by 2 publications

References 11 publications

max-projective modules

max-projective modules

Max-projective modules

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