Geodesic
Characterizations of right Nakayama rings
Glasgow mathematical journal, Tome 34 (1992) no. 1, pp. 91-102

Voir la notice de l'article provenant de la source Cambridge University Press

We have studied relationships between almost relative projectivity and Nakayamaings [8]. In this paper we shall further investigate certain characterizations of right Nakayama rings in terms of almost relative projectives (or injectives). We shall consider three conditions (A), (B) and (C) (see Section 1), which are always satisfied for the relative projective modules, but not for almost relative projectives in general. As an application of [9, Theorem] and [10, Theorem 2], we shall show that a right artinian ring is right Nakayama if and only if one of the above three conditions holds true for almost relative projectives (Corollary to Theorem 1). Moreover we shall give a characterization of two-sided Nakayama rings related to (C) and the dual (C#) (Theorem 2). Finally we shall investigate the transitivity of almost relative projectives, which is the converse of (B), and give some characterizations of right Nakayama rings related to the transitivity. 
Harada, Manabu. Characterizations of right Nakayama rings. Glasgow mathematical journal, Tome 34 (1992) no. 1, pp. 91-102. doi: 10.1017/S0017089500008570
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[1] 1.Albu, T. and Nastasescu, C., Relative finiteness in module theory, Monographs and Textbooks in Pure and Applied Mathematics 84 (Marcel Dekker, 1984). Google Scholar

[2] 2.Azumaya, G., Mbuntum, F. and Varadarajan, K., On M-projective and M-injective modules, Pacific J. Math. 59 (1975), 9–16. Google Scholar | DOI

[3] 3.Fuller, K. R., On indecomposable injectives over artinian rings, Pacific J. Math. 29 (1969), 115–135. Google Scholar | DOI

[4] 4.Baba, Y., Note on almost M-injectives, Osaka J. Math. 26 (1989), 687–698. Google Scholar

[5] 5.Baba, Y. and Harada, M., On almost relative projectives and injectives, Tsukuba Math. J. 14 (1990), 53–69. Google Scholar | DOI

[6] 6.Harada, M., Uniserial rings and lifting properties, Osaka J. Math. 19 (1982), 217–229. Google Scholar

[7] 7.Harada, M., Generalization of Nakayama ring III, Osaka J. Math. 23 (1986), 523–539. Google Scholar

[8] 8.Harada, M. and Tozaki, A., Almost M-projectives and Nakayama rings, J. Algebra 122 (1989), 447–474. Google Scholar | DOI

[9] 9.Harada, M., On almost relative projectives over perfect rings, Osaka J. Math. 27 (1990), 465–482. Google Scholar

[10] 10.Harada, M., On almost relative injectives on artinian modules, Osaka J. Math. 27 (1990), 963–971. Google Scholar

[11] 11.Harada, M. and Mabuchi, T., On almost M-projectives, Osaka J. Math. 26 (1989), 837–848. Google Scholar

[12] 12.Harada, M., Hereditary rings and almost relative projectives, to appear. Google Scholar

[13] 13.Oshiro, K., Semiperfect modules and quasi-semiperfect modules, Osaka J. Math. 20 (1983), 337–373. Google Scholar

[14] 14.Sumioka, T., Tachikawa's theorem on algebras of left colocal type, Osaka J. Math. 21 (1984), 629–648. Google Scholar

[15] 15.Sumioka, T., On artinian ring of right local type, Math. J. Okayama Univ. 29 (1987), 127–146. Google Scholar

[16] 16.Wisbauer, R., Grundlagen der Modul- und Ringtheorie. Ein Handbuch für Studium and Forschung (Reinhard Fischer, 1988). Google Scholar

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