Modules satisfying conditions that are opposites of absolute purity and flatness
Kafkas Demirci, Gizem, author.

Modules satisfying conditions that are opposites of absolute purity and flatness

Kafkas Demirci, Gizem, author.

Yazar Ek Girişi
Kafkas Demirci, Gizem, author.

Fiziksel Tanımlama
viii, 61 leaves:+ 1 computer laser optical disc.

The main purpose of this thesis is to study the properties which are opposites of absolute pure and flat modules. A right module M is said to be test for flatness by subpurity (for short, t.f.b.s.) if its subpurity domain is as small as possible, namely, consisting of exactly the flat left modules. A left module M is said to be rugged if its flatness domain is the class of all regular right R-modules. Every ring has a t.f.b.s. module. For a right Noetherian ring R every simple right R-module is t.f.b.s. or absolutely pure if and only if R is a right V-ring or R A×B, where A is right Artinian with a unique non-injective simple right R-module and Soc(AA) is homogeneous and B is semisimple. A characterization of t.f.b.s. modules over commutative hereditary Noetherian rings is given. Rings all (cyclic) modules of whose are rugged are shown to be von Neumann regular rings. Over a right Noetherian ring every left module is rugged or flat if and only if every right module is poor or injective if and only if R = S × T, where S is semisimple Artinian and T is either Morita equivalent to a right PCI-domain, or T is right Artinian whose Jacobson radical contains no properly nonzero ideals. Connections between rugged and poor modules are shown. Rugged Abelian groups are fully characterized.

Konu Başlığı
Modules (Algebra).

Yazar Ek Girişi
Büyükaşık, Engin,

Tüzel Kişi Ek Girişi
İzmir Institute of Technology. Mathematics.

Tek Biçim Eser Adı
Thesis (Doctoral)--İzmir Institute of Technology:Mathematics.
İzmir Institute of Technology:Mathematics--Thesis (Doctoral).

Elektronik Erişim
Access to Electronic Versiyon.

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