FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1995, VOLUME 1, NUMBER 2, PAGES 471-489

Serial Krull-Schmidt rings and pure-injective modules

G.E.Puninski

A ring is called Krull-Schmidt if every finitely presented module over it can be decomposed into direct sum of modules with local endomorphism rings. The serial Krull-Schmidt rings are described as rings with the weak invariance condition. The classification of indecomposable pure-injective modules over uniserial ring is simplified and criteria for the existence of superdecomposable pure-injective module is given for semi-invariant case. Let T be the theory of all modules over effectively given invariant uniserial ring R with infinite residue skew field. It is shown that T is decidable if the question of invertibility of element from R can be solved effectively.

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Last modified: October 3, 1997.