Neredeyse mükemmel halkalar

Bazzoni and Salce have showed that all modules over a commutative domain R have a strongly flat cover if and only if every flat R-module is strongly flat and that holds if and only if R is almost perfect, that is, every proper quotient of R is a perfect ring. Facchini and Parolin defined a ring R to be right almost perfect if the quotient ring R/I is a right perfect ring for every nonzero proper two-sided ideal I of R. They proved that most of the properties of commutative almost perfect domains still hold in the noncommutative setting. In this thesis, we observe the relation between commutative almost perfect domains and C-rings of Renault, and then the relation between right almost perfect rings and C-J-rings of Generalov. A ring R is said to be a left C-ring if for every left R-module M and for every essential proper submodule N of M, M/N has a simple submodule. For a set J of left ideals of a ring R, the ring R is said to be a left C-J-ring if for any proper J-dense left ideal I of R (that is, for every element r of R, the left ideal (I:r) belongs to J and (I:r)r is not equal to 0), there exists an element r of R such that (I:r) is a maximal left ideal. Facchini and Parolin have defined h-locality also for noncommutative rings. A ring R is said to be h-local if R/I is semilocal for every proper nonzero two-sided ideal I of R and every nonzero prime two-sided ideal of R is contained in a unique maximal two-sided ideal of R. We prove that for a prime ring R, R is right almost perfect if and only if it is h-local and a left C-J-ring, where J is the Gabriel filter that consists of the left ideals I of R such that for every two-sided ideal J containing I properly, there exists an element r not contained in J with (J:r) containing a nonzero two-sided ideal.