Noetherian rings can be extended to finitely presented modules over coherent rings. Every left Noetherian ring is left coherent. The ring of polynomials...

coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information. Coherent sheaves can be seen as a generalization of vector...

and coherent modules all of which are defined below. Over a Noetherian ring the concepts of finitely generated, finitely presented and coherent modules...

the spectrum of a commutative ring. It is sometimes also called a coherent space because of the connection to coherent topoi. Let X be a topological space...

Noetherian integral domain is a Dedekind ring with a torsion class group.: 200  A coherent ring is a commutative ring with each finitely generated ideal finitely...

general be flat. In fact, given a ring R, every direct product of flat R-modules is flat if and only if R is a coherent ring (that is, every finitely generated...

intensity). The system can accommodate coherent units for an unlimited number of additional quantities. These are called coherent derived units, which can always...

problems considered here make sense only for a Noetherian ring, or at least a coherent ring. In fact, this article is restricted to Noetherian integral...

wavelength 3.6 cm near ring's apoapsis. Such strong scattering requires the existence of a coherent structure. That the ε ring does have such a fine structure...

mathematics, a ringed space is a family of (commutative) rings parametrized by open subsets of a topological space together with ring homomorphisms that...