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Self-injective and PF endomorphism rings. (English) Zbl 0627.16025

The authors study the endomorphism ring S of a \(\Sigma\)-quasiprojective module M, providing necessary and sufficient conditions on M for S to have certain properties such as, e.g. being QF or left (F)PF.
Reviewer: C.Năstăsescu

MSC:

16S50 Endomorphism rings; matrix rings
16D50 Injective modules, self-injective associative rings
16B50 Category-theoretic methods and results in associative algebras (except as in 16D90)
Full Text: DOI

References:

[1] Albu, T.; NĂstĂsescu, C., Relative Finiteness in Module Theory, Pure and Applied Mathematics, Vol. 84 (1984), New York: Marcel Dekker, New York · Zbl 0556.16001
[2] Anderson, F. W.; Fuller, K. R., Rings and Categories of Modules (1974), New York: Springer-Verlag, New York · Zbl 0301.16001
[3] Faith, C.; Page, S., FPF Ring Theory (1984), Cambridge: Cambridge University Press, Cambridge · Zbl 0554.16007
[4] García Hernández, J. L.; Gómez Pardo, J. L., Hereditary and semihereditary endomorphism rings, Ring Theory Proceedings, Antwerp 1985, 83-89 (1986), Berlin: Springer-Verlag, Berlin · Zbl 0597.16022
[5] J. L. García Hernández and J. L. Gómez Pardo,On endomorphism rings of quasiprojective modules, Math. Z., to appear. · Zbl 0562.16012
[6] García Hernández, J. L.; Gómez Pardo, J. L.; Martínez Hernández, J., Semiperfect modules relative to a torsion theory, J. Pure Appl. Algebra, 43, 145-172 (1986) · Zbl 0608.16024 · doi:10.1016/0022-4049(86)90092-7
[7] Golan, J., Localization of Noncommutative Rings (1975), New York: Marcel Dekker, New York · Zbl 0302.16002
[8] Gómez Pardo, J. L.; Martínez Hernández, J., Coherence of endomorphism rings, Arch. Math., 48, 40-52 (1987) · Zbl 0586.16013 · doi:10.1007/BF01196353
[9] G. Hauger and W. Zimmermann,Lokalisierung, Vervollständigung von Ringen und Bikommutatoren von Moduln, Algebra Bericht Nr. 18, Math. Inst. Univ. München, 1974. · Zbl 0313.16004
[10] Kasch, F., Modules and Rings (1982), London: Academic Press, London · Zbl 0523.16001
[11] Kato, T., Torsionless modules, Tôhoku Math. J., 20, 234-243 (1968) · Zbl 0175.31802
[12] Kato, T., U-distinguished modules, J. Algebra, 25, 15-24 (1973) · Zbl 0252.16006 · doi:10.1016/0021-8693(73)90072-0
[13] Nita, C., Sur l’anneau des endomorphismes d’un module générateur projectif, J. Algebra, 49, 149-153 (1977) · Zbl 0381.16009 · doi:10.1016/0021-8693(77)90274-5
[14] Onodera, T., Ein Satz über koendlich erzeugte RZ-Moduln, Tôhoku Math. J., 23, 691-695 (1971) · Zbl 0237.16019
[15] Page, S. S., FPF endomorphism rings with applications to QF-3 rings, Commun. Algebra, 14, 423-435 (1986) · Zbl 0592.16012 · doi:10.1080/00927878608823315
[16] Popescu, N., Abelian Categories with Applications to Rings and Modules (1973), London: Academic Press, London · Zbl 0271.18006
[17] Rutter, E. A., PF-modules, Tôhoku Math. J., 23, 201-206 (1971) · Zbl 0218.16005
[18] Sandomierski, F. L., Modules over the endomorphism ring of a finitely generated projective module, Proc. Amer. Math. Soc., 31, 27-31 (1972) · Zbl 0233.16021 · doi:10.2307/2038506
[19] Stenström, B., Rings of Quotients (1975), Berlin: Springer-Verlag, Berlin · Zbl 0296.16001
[20] Wagoner, R. L., Cogenerator endomorphism rings, Proc. Amer. Math. Soc., 28, 347-351 (1971) · Zbl 0214.29203 · doi:10.2307/2037966
[21] Wisbauer, R., Localization of modules and the central closure of rings, Commun. Algebra, 9, 1455-1493 (1981) · Zbl 0461.16020 · doi:10.1080/00927878108822655
[22] B. Zimmermann,Endomorphism Rings of Self-generators, Algebra Bericht Nr. 27, Math. Inst. Univ. München, 1975.
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