Başlık:

When certain relative projectivity and injectivity conditions imply the global projectivity and injectivity

Yazar:

Benli Göral, Sinem, author.

Yazar Ek Girişi:

Fiziksel Tanımlama:

vi, 57 leaves:+ 1 computer laser optical disc.

Özet:

A right R-module M is called R-projective provided that it is projective relative to the right R-module RR. One of the parts of this thesis deals with the rings whose all nonsingular right modules are R-projective. For a right nonsingular ring R, we prove that RR is of finite Goldie rank and all nonsingular right R-modules are R-projective if and only if R is right finitely Σ-CS and flat right R-modules are R-projective. Then, R-projectivity of the class of nonsingular injective right modules is also considered. Over right nonsingular rings of finite right Goldie rank, it is shown that R-projectivity of nonsingular injective right modules is equivalent to R-projectivity of the injective hull E(RR). As a second goal, we deal with simple-injective modules. For a right module M, we prove that M is simple-injective if and only if M is min-N-injective for every cyclic right module N. The rings whose simple-injective right modules are injective are exactly the right Artinian rings. A right Noetherian ring is right Artinian if and only if every cyclic simple-injective right module is injective. The ring is quasi-Frobenius if and only if simple-injective right modules are projective. For a commutative Noetherian ring R, we prove that every finitely generated simple-injective R-module is projective if and only if R = A × B, where A is quasi-Frobenius and B is hereditary. An abelian group is simpleinjective if and only if its torsion part is injective.

Konu Başlığı:

Yazar Ek Girişi:

Tüzel Kişi Ek Girişi:

Tek Biçim Eser Adı:

Thesis (Doctoral)--İzmir Institute of Technology:Mathematics.

İzmir Institute of Technology: Mathematics--Thesis (Doctoral).

Elektronik Erişim:

Access to Electronic Versiyon.Copies:

### Rafta:*

Kütüphane | Materyal Türü | Demirbaş Numarası | Yer Numarası | Durumu/İade Tarihi |
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Arıyor... | Tez | T002572 | QA251.4 .B46 2022 | Arıyor... |