Displaying similar documents to “Projectivity and flatness over the endomorphism ring of a finitely generated comodule.”

Finite presentation and purity in categories σ[M]

Mike Prest, Robert Wisbauer (2004)

Colloquium Mathematicae

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For any module M over an associative ring R, let σ[M] denote the smallest Grothendieck subcategory of Mod-R containing M. If σ[M] is locally finitely presented the notions of purity and pure injectivity are defined in σ[M]. In this paper the relationship between these notions and the corresponding notions defined in Mod-R is investigated, and the connection between the resulting Ziegler spectra is discussed. An example is given of an M such that σ[M] does not contain any non-zero finitely...

Rings with zero intersection property on annihilators: Zip rings.

Carl Faith (1989)

Publicacions Matemàtiques

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Zelmanowitz [12] introduced the concept of ring, which we call right zip rings, with the defining properties below, which are equivalent: (ZIP 1) If the right anihilator X⊥ of a subset X of R is zero, then X1 ⊥ = 0 for a finite subset X1 ⊆ X. (ZIP 2) If L is a left ideal and if L⊥ = 0, then L1 ...