Strongly noncosingular modules
by
Alagöz, Yusuf, author.
Title
:
Strongly noncosingular modules
Author
:
Alagöz, Yusuf, author.
Personal Author
:
Alagöz, Yusuf, author.
Physical Description
:
vii, 39 leaves:+ 1 computer laser optical disc.
Abstract
:
The main purpose of this thesis is to investigate the notion of strongly noncosingular modules. We call a right R-module M strongly noncosingular if for every nonzero right RmoduleN and every nonzero homomorphismf : M → N, Im(f) is not a cosingular (or Radsmall) submodule of N in the sense of Harada. It is proven that (1) A right R-module M is strongly noncosingular if and only ifM is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective right R-modules coincides with the class of (strongly) noncosingular right R-modules; (3) a right hereditary ring R is Max-ring if and only if absolutely coneat right R-modules are strongly noncosingular; (4) a commutative ring R is semisimple if and only if the class of injective R-modules coincides with the class of strongly noncosingular R-modules.
Subject Term
:
Modules (Algebra)
Rings (Algebra)
Added Author
:
Büyükaşık, Engin.
Added Corporate Author
:
İzmir Institute of Technology. Mathematics.
Added Uniform Title
:
Thesis (Master)--İzmir Institute of Technology:Mathematics.
İzmir Institute of Technology:Mathematics--Thesis (Master).
Electronic Access
:
Library | Material Type | Item Barcode | Shelf Number | Status |
---|
IYTE Library | Thesis | T001259 | QA247.3 .A43 2014 | Tez Koleksiyonu |
IYTE Library | Supplementary CD-ROM | ROM2274 | QA247.3 .A43 2014 EK.1 | Tez Koleksiyonu |