×

Dominant modules and finite localizations. (English) Zbl 0439.16005


MSC:

16P50 Localization and associative Noetherian rings
16D40 Free, projective, and flat modules and ideals in associative algebras
16D80 Other classes of modules and ideals in associative algebras
16L60 Quasi-Frobenius rings
Full Text: DOI

References:

[1] F. W. ANDERSON, Endomorphism rings of projective modules, Math. Z. III (1969), 322-332. · Zbl 0179.33903 · doi:10.1007/BF01110241
[2] H. BASS, Algebraic ^-theory, Benjamin, New York; 1968 · Zbl 0174.30302
[3] J. A. BEACHY, Cotorsion radicals and projective modules, Bull. Austral. Math. Soc. (1971), 241-253. · Zbl 0218.16009 · doi:10.1017/S0004972700047122
[4] H. CARTAN AND S. EILENBERG, Homological algebra, Princeton University Press, Prince ton, New Jersey; 1956. · Zbl 0075.24305
[5] R. R. COLBY AND E. A. RUTTER, JR., The structure of certain artinian rings with zer singular ideal, J. Algebra 8 (1968), 156-164. ]6] R. R. COLBY AND E. A. RUTTER, JR., QF-3 rings with zero singular ideal, Pacific J. Math. 28 (1969), 303-308. · Zbl 0221.16018 · doi:10.1016/0021-8693(68)90041-0
[6] R. R. COLBY AND E. A. RUTTER. JR., Generalizations of QF-3 algebras, Trans. Amer Math. Soc. 153 (1971), 371-386. JSTOR: · Zbl 0211.36105 · doi:10.2307/1995563
[7] R. S. CUNNINGHAM, E. A. RUTTER, JR. AND D. R. TURNIDGE, Rings of quotients o endomorphism rings of projective modules, Pacific J. Math. 41 (1972), 647-668. · Zbl 0215.37903 · doi:10.2140/pjm.1972.41.647
[8] C. FAITH, Lectures on injective modules, Lecture notes in Mathematics No. 49, Springer Verlag, Berlin, Heidelberg, New York; 1967. · Zbl 0162.05002 · doi:10.1007/BFb0074319
[9] J. P. JANS, Some aspects of torsion, Pacific J. Math. 15 (1965), 1249-1259 · Zbl 0142.28002 · doi:10.2140/pjm.1965.15.1249
[10] T. KATO, Some generalizations of QF-rings, Proc. Japan Acad. 44 (1968), 114-119 · Zbl 0162.33801 · doi:10.3792/pja/1195521293
[11] T. KATO, Torsionless modules, Thoku Math. J. 20 (1968), 234-243 · Zbl 0175.31802 · doi:10.2748/tmj/1178243180
[12] T. KATO, Dominant modules, J. Algebra 14 (1970), 341-349 · Zbl 0191.04001 · doi:10.1016/0021-8693(70)90110-9
[13] T. KATO, Structure of left QF-3 rings, Proc. Japan Acad. 48 (1972), 479-483 · Zbl 0251.16013 · doi:10.3792/pja/1195519593
[14] T. KATO, {/-dominant dimension and {/-localization (unpublished)}} · Zbl 0051.09203
[15] J. LAMBEK, Lectures on rings and modules, Blaisdell, Waltham, Massachusetts; 1966 · Zbl 0143.26403
[16] K. MASAIKE, On quotient rings and torsionless modules, Sci. Rep. Tokyo Kyoiku Daigaku, Sec. All, No. 280, (1971), 26-30. · Zbl 0235.16001
[17] K. MORITA, Duality for modules and its applications to rings with minimum condition, Sci. Rep. Tokyo Kyoiku Daigaku, Sec. A6, No. 150 (1958), 83-142. · Zbl 0080.25702
[18] K. MORITA, On S-rings, Nagoya Math. J. 27 (1966), 687-695 · Zbl 0139.25804
[19] B. L. OSOFSKY, A generalization of quasi-Frobenius rings, J. Algebra 4 (1966), 373-387 · Zbl 0171.29303 · doi:10.1016/0021-8693(66)90028-7
[20] C. M. RINGEL AND H. TACHIKAWA, QF-3 rings, J. Reine Angew. Math. 272 (1975), 49-72 · Zbl 0318.16006
[21] B. Roux, Sur la dualite de Morita, Thoku Math. J. 23 (1971), 457-472 · Zbl 0233.16016 · doi:10.2748/tmj/1178242594
[22] E. A. RUTTER, JR., PF and QF-3 rings, Arch. Math. 20 (1969), 262-266 · Zbl 0184.06501 · doi:10.1007/BF01899297
[23] E. A. RUTTER, JR., PF-modules, Thoku Math. J. (1971), 201-206 · Zbl 0218.16005 · doi:10.2748/tmj/1178242640
[24] E. A. RUTTER, JR., QF-3 rings with ascending chain condition on annihilators, J. Rein Angew. Math, (to appear). · Zbl 0309.16013 · doi:10.1515/crll.1975.277.40
[25] F. L. SANDOMIERSKI, Modules over the endomorphism ring of a finitely generated projec tive module, Proc. Amer. Math. Soc. 31 (1972), 27-31. JSTOR: · Zbl 0233.16021 · doi:10.2307/2038506
[26] L. SILVER, Noncommutative localizations and applications, J. Algebra 7 (1967) 44-76 · Zbl 0173.03305 · doi:10.1016/0021-8693(67)90067-1
[27] B. STENSTROM, Rings and modules of quotients, Lecture Notes in Mathematics No. 177 Springer-Verlag, Berlin, Heidelberg, New York; 1971.
[28] H. H. STORRER, Rings of quotients of perfect rings, Math. Z. 122 (1971), 151-165 Zentralblatt MATH: · Zbl 0214.05302 · doi:10.1007/BF01110089
[29] R. WARE, Endomorphism rings of projective modules, Trans. Amer. Math. Soc. 155 (1971), 233-259. JSTOR: · Zbl 0215.09101 · doi:10.2307/1995475
[30] J. ZELMANOWITZ, Injective hulls of torsion free modules, Can. J. Math. 23 (1971), 1094 1101. Zentralblatt MATH: · Zbl 0222.16023 · doi:10.4153/CJM-1971-115-x
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.