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Duality for quotient modules and a characterization of reflexive modules. (English) Zbl 0512.16021


MSC:

16D90 Module categories in associative algebras
16S90 Torsion theories; radicals on module categories (associative algebraic aspects)
16D80 Other classes of modules and ideals in associative algebras
16P60 Chain conditions on annihilators and summands: Goldie-type conditions
16Exx Homological methods in associative algebras
Full Text: DOI

References:

[1] Azumaya, G., A duality theory for injective modles, Amer. J. Math., 81, 249-278 (1959) · Zbl 0088.03304
[2] Bass, H., Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc., 95, 466-488 (1960) · Zbl 0094.02201
[3] Colby, R. R.; Rutter, E. A., Generalizations of QF-3 algebras, Trans. Amer. Math. Soc., 153, 371-385 (1973) · Zbl 0211.36105
[4] Golan, J. S., Localizations of Noncommutative Rings, (Pure and Applied Math., Vol. 30 (1975), Marcel Dekker: Marcel Dekker New York) · Zbl 0199.35502
[5] Goldman, O., Elements of noncommunicative arithmetic 1, J. Algebra, 35, 308-341 (1965) · Zbl 0313.16002
[6] Kato, T., Structure of dominant modules, J. Algebra, 39, 563-570 (1976) · Zbl 0325.16017
[7] Lambek, J., Torsion Theories, (Additive Semantics and Rings of Quotients. Additive Semantics and Rings of Quotients, Lecture Notes in Mathematics, 177 (1971), Springer: Springer Berlin-New York) · Zbl 0213.31601
[8] Masaike, K., On quotient rings and torsionless modules, Sci. Rep. Tokyo Kyoiku Daigaku, 11, 26-31 (1971), Sec. A · Zbl 0235.16001
[9] Masaike, K., Semi-primary QF-3 quotient rings, Comm. in Algebra, 11, 4 (1983) · Zbl 0511.16004
[10] Miller, R. W.; Teply, M. L., The descending chain condition relative to a torsion theory, Pacific J. Math., 83, 207-218 (1979) · Zbl 0444.16017
[11] Morita, K., Duality for modules and its applications to the theory of rings with minimum condition, Sci. Rep. Tokyo Kyoiku Daigaku Sec. A, 6, 83-142 (1958) · Zbl 0080.25702
[12] Morita, K., Duality in QF-3 rings, Math. Z., 108, 237-252 (1968) · Zbl 0169.35701
[13] Rutter, E. A., Dominant modules and finite localizations, Tohoku Math. J., 27, 225-239 (1975) · Zbl 0439.16005
[14] Rutter, E. A., QF-3 rings with ascending chain condition on annihilators, J. Reine Angew. Math., 277, 40-44 (1975) · Zbl 0309.16013
[15] Stenström, B., Rings of Quotients, (Grund. Math. Wiss., Vol. 217 (1975), Springer: Springer Berlin) · Zbl 0194.06602
[16] Sumioka, T., On non-singular QF-3 rings with injective dimension ≤1, Osaka J. Math., 15, 1-11 (1978) · Zbl 0391.16012
[17] Tachikawa, H., Quasi-Frobenius Rings and Generalizations, (Lecture Notes in Math., 351 (1973), Springer: Springer Berlin) · Zbl 0177.05901
[18] Tachikawa, H., Duality theorem of character modules for rings with minimum condition, Math. Z., 68, 479-487 (1958) · Zbl 0222.16022
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