Geodesic
Serial Krull–Schmidt rings and pure-injective modules
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 2, pp. 471-489 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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G. E. Puninskii. Serial Krull–Schmidt rings and pure-injective modules. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 2, pp. 471-489. http://geodesic.mathdoc.fr/item/FPM_1995_1_2_a8/

[1] Drozd Yu. A., “Ob obobschenno odnoryadnykh koltsakh”, Matem. zametki, 18:5 (1975), 705–710 | MR | Zbl

[2] Puninskii G. E., “Superrazlozhimye chisto-in'ektivnye moduli nad kommutativnymi koltsami normirovaniya”, Sib. matem. zh., 31:6 (1990), 655–671 | MR

[3] Puninskii G. E., “Nerazlozhimye chisto-in'ektivnye moduli nad tsepnymi koltsami”, Trudy Mosk. matem. obschestva, 56, 1994, 1–13

[4] Puninskii G. E., “Odno zamechanie o chisto-in'ektivnykh modulyakh nad polutsepnym koltsom”, Uspekhi matem. nauk, 49:5 (1994), 171–172 | MR | Zbl

[5] Bessenrodt K., Brungs H. H., Törner G., Right serial rings. Part 1, Preprint, 1990

[6] Camps R., Dicks W. On semilocal rings, Israel J. Math., 81 (1993), 203–211 | DOI | MR | Zbl

[7] Eklof P., Herzog I, A Some model theory over a serial ring, Preprint, 1993

[8] Eklof P., Sabbagh G. “Model completions and modules”, Ann. Math. Logic, 2:3 (1971), 251–295 | DOI | MR | Zbl

[9] Herzog I., A test for finite representation type, Preprint, 1993 | MR

[10] McConnell J. C., Robson J. C., Noncommutative noetherian rings, New York, 1988

[11] Mohamed S. H., Müller B. J., Continuous and discrete modules, Cambridge, 1990 | MR

[12] Müller B. J., Singh S., “Uniform modules over serial rings”, J. Algebra, 144 (1991), 94–109 | DOI | MR | Zbl

[13] Prest M., Model theory and modules, Cambridge, 1988 | MR

[14] Puninski G. E., “Pure-injective modules over right Noetherian serial rings”, Comm. Algebra, 23:4 (1995), 1579–1591 | DOI | MR | Zbl

[15] Rothmaler Ph., “A trivial remark on purity”, Seminarber. Fachber, 112, Humbold Univ., Berlin, 1991, 112–127

[16] Stephenson W., “Modules whose lattice of submodules is distributive”, Proc. Lond. Math. Soc., Ser. 3, 28:2 (1974), 291–310 | DOI | MR | Zbl

[17] Warfield R. B., “Serial rings and finitely presented modules”, J. Algebra, 37:3 (1975), 187–222 | DOI | MR | Zbl