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Content Modules and Algebras.
The Dedekind-Mertens lemma and the contents of polynomials
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
Strongly irreducible ideals of a commutative ring
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 irreducibleExpand
Rings with two-generated ideals
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 overExpand
Two-Generated Ideals and Representations of Abelian Groups over Valuation Rings
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 nExpand
Basically Full Ideals in Local Rings
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 aExpand
Strongly Prime Submodules, G-Submodules and Jacobson Modules
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 includingExpand
The conditionsInt(R) ⊆ RS[X] andInt(RS) = Int(R)S for integer-valued polynomials
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 weExpand