Let be a set of ideals of a commutative Noetherian ring . We use the notion of -closure operation which is a semiprime closure operation on submodules of modules to introduce the class of -Laskerian modules. This enables us to investigate the set of associated prime ideals of certain -closed submodules of local cohomology modules.
Let D be an integral domain with field of fractions K. In this article, we use a certain pullback construction in the spirit of Int(E,D) that furnishes many examples of domains between D[x] and K[x] in which there are elements that do not admit a finite factorization into irreducible elements. We also define the notion of a fixed divisor for this pullback construction to characterize all of its irreducible elements and those nonzero nonunits that do admit a finite factorization into irreducibles....
2000 Mathematics Subject Classification: 17A50, 05C05.In this note we present the formula for the coefficients of the substitution series f(g(x)) of planar tree power series g(x) into f(x).
Let be a commutative ring with identity. If a ring is contained in an arbitrary union of rings, then is contained in one of them under various conditions. Similarly, if an arbitrary intersection of rings is contained in , then contains one of them under various conditions.