… coherent and J-coherent rings. For instance, we prove that R is a left J-coherent ring if and
only if … As a consequence, we get that every left R-module over a left J-coherent ring R has a J-…

… rings, left semihereditary rings and their generalizations have been studied by many authors.
For example, a ring R is said to be left J-coherent … ., projective); a ring R is said to be left n-…

… -coherent rings, where X is a class of modules and n is a positive integer, as those rings for
… submodules of the Jacobson radical, the 0-X -coherent rings are called J-coherent (see [8]). …

… presented; a ring R is called left min-coherent [19] if every minimal left ideal is finitely
presented; a ring R is called left J-coherent [8… Then R is C-coherent if and only if R is left J-coherent. …

… ring R is called an n-von-Neumann regular ring [14] if … rings and left J-coherent rings to left
In-coherent rings. The concepts of left n-semihereditary rings and left J-semihereditary rings …

… ring in the literature, we find the following, due to Ding, Li and Mao [14]. A ring R is said to be
a J-coherent ring … Clearly, any coherent ring is a J-coherent ring, but the converse is false. In …

… We also show that, if R is a uniformly gr-coherent ring and I is a finitely generated … ring. We
also show that, a finite direct sum of uniformly gr-coherent rings is a uniformly gr-coherent ring. …

… The graded ring R is said to be a uniformly gr-coherent ring if it is uniformly gr-coherent as a
graded … gr-coherent rings (and modules) that we call weakly uniformly grcoherent rings (and …

… are introduced, in this paper, as the generalization of Jcoherent rings and semiprime
rings. Some examples of left Nil∗-coherent rings are given, and some properties of left Nil∗-…

… If R n is a J -coherent ring, then J ( R n ) = θ K [ θ ] is coherent. … and a QF ring, which implies
R n is also a J -coherent ring. … Suppose that R n is a J -coherent ring. Since J ( R n ) = J ( D ) + …