Let R be a commutative ring, let X be an indeterminate, and let g E R[X]. There has been much recent work concerned with determining the Dedekind-Mertens number P,R(g)=min{k E N I cR(f)k-lcR(fg) =… Expand

Abstract An ideal I of a ring R is said to be strongly irreducible if for ideals J and K of R, the inclusion J∩K⊆I implies that either J⊆I or K⊆I. The relationship among the families of irreducible… Expand

Abstract A commutative ring R is said to have the two-generator property if each ideal of R can be generated by two elements, and is said to be stable if each regular ideal of R is projective over… Expand

Abstract Let R be a commutative ring with identity. We give some general results on non-Noetherian commutative rings with the property that each finitely generated ideal can be generated by n… Expand

Abstract Let A be a finitely generated module over a (Noetherian) local ring ( R , M ). We say that a nonzero submodule B of A is basically full in A if no minimal basis for B can be extended to a… Expand

Some characterizations are given of A. R. Naghipour's strongly prime submodules among the prime submodules of a finitely generated R-module M, together with some consequences of these including… Expand

Abstract Let R be an integral domain with quotient field K and let Int(R) = { f e K[X]| f(R) ⊆ R }. In this note we determine when Int(R) = R[X] for an arbitrary integral domain R . More generally we… Expand