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## Homological objects of proper classes generated by simple modules

##### Abstract

The main purpose of this thesis is to study some classes of modules determined
by neat, coneat and s-pure submodules. A right R-module M is called neat-flat (resp.
coneat-flat) if the kernel of any epimorphism Y → M → 0 is neat (resp. coneat) in Y. A
right R-module M is said to be absolutely s-pure if it is s-pure in every extension of it. If
R is a commutative Noetherian ring, then R is C-ring if and only if coneat-flat modules
are flat. A commutative ring R is perfect if and only if coneat-flat modules are projective.
R is a right
Σ
-CS ring if and only if neat-flat right R-modules are projective. R is a right
Kasch ring if and only if injective right R-modules are neat-flat if and only if the injective
hull of every simple right R-module is neat-flat. If R is a right N-ring, then R is right
Σ
-CS ring if and only if pure-injective neat-flat right R-modules are projective if and
only if absolutely s-pure left R-modules are injective and R is right perfect. A domain R
is Dedekind if and only if absolutely s-pure modules are injective. It is proven that, for
a commutative Noetherian ring R, (1) neat-flat modules are flat if and only if absolutely
s-pure modules are absolutely pure if and only if R A × B, wherein A is QF-ring and B
is hereditary; (2) neat-flat modules are absolutely s-pure if and only if absolutely s-pure
modules are neat-flat if and only if R A × B, wherein A is QF-ring and B is Artinian
with J2(B) = 0.

##### Collections

- Phd Degree / Doktora [292]