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On torsion Gorenstein injective modules

Okyeon Yi (1998)

Archivum Mathematicum

In this paper, we define Gorenstein injective rings, Gorenstein injective modules and their envelopes. The main topic of this paper is to show that if D is a Gorenstein integral domain and M is a left D -module, then the torsion submodule t G M of Gorenstein injective envelope G M of M is also Gorenstein injective. We can also show that if M is a torsion D -module of a Gorenstein injective integral domain D , then the Gorenstein injective envelope G M of M is torsion.

Polynômes de Barsky

Youssef Haouat, Fulvio Grazzini (1979)

Annales scientifiques de l'Université de Clermont. Mathématiques

Polynomial rings over Jacobson-Hilbert rings.

Carl Faith (1989)

Publicacions Matemàtiques

All rings considered are commutative with unit. A ring R is SISI (in Vámos' terminology) if every subdirectly irreducible factor ring R/I is self-injective. SISI rings include Noetherian rings, Morita rings and almost maximal valuation rings ([V1]). In [F3] we raised the question of whether a polynomial ring R[x] over a SISI ring R is again SISI. In this paper we show this is not the case.

Precobalanced and cobalanced sequences of modules over domains

Anthony Giovannitti, H. Pat Goeters (2007)

Mathematica Bohemica

The class of pure submodules ( 𝒫 ) and torsion-free images ( ) of finite direct sums of submodules of the quotient field of an integral domain were first investigated by M. C. R. Butler for the ring of integers (1965). In this case 𝒫 = and short exact sequences of such modules are both prebalanced and precobalanced. This does not hold for integral domains in general. In this paper the notion of precobalanced sequences of modules is further investigated. It is shown that as in the case for abelian groups...

Prescribing endomorphism algebras of n -free modules

Rüdiger Göbel, Daniel Herden, Saharon Shelah (2014)

Journal of the European Mathematical Society

It is a well-known fact that modules over a commutative ring in general cannot be classified, and it is also well-known that we have to impose severe restrictions on either the ring or on the class of modules to solve this problem. One of the restrictions on the modules comes from freeness assumptions which have been intensively studied in recent decades. Two interesting, distinct but typical examples are the papers by Blass [1] and Eklof [8], both jointly with Shelah. In the first case the authors...

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