On relative projectivity of some classes of modules
by
Alagöz, Yusuf, author.
Title
:
On relative projectivity of some classes of modules
Author
:
Alagöz, Yusuf, author.
Personal Author
:
Alagöz, Yusuf, author.
Physical Description
:
vii, 67 leaves:+ 1 computer laser optical disc.
Abstract
:
The main purpose of this thesis is to study R-projectivity and max-projectivity of some classes of modules, and module classes related to max-projective modules. 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). In this thesis we attempt 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 x 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 x B, where A is QF and B is a small ring. Moreover, we introduced and studied some homological objects related with max-projective modules.
Subject Term
:
Injective modules (Algebra).
Modules (Algebra).
Added Author
:
Büyükaşık, Engin
Added Corporate Author
:
İzmir Institute of Technology. Mathematics.
Added Uniform Title
:
Thesis (Doctoral)--İzmir Institute of Technology:Mathematics.
İzmir Institute of Technology:Mathematics--Thesis (Doctoral).
Electronic Access
:
Library | Material Type | Item Barcode | Shelf Number | Status |
---|
IYTE Library | Thesis | T002050 | QA247 .A31 2019 | Tez Koleksiyonu |
IYTE Library | Supplementary CD-ROM | ROM3210 | QA247 .A31 2019 EK.1 | Tez Koleksiyonu |