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A ring R is called left max-coherent provided that every maximal left ideal is finitely presented. MI (resp. MF) denotes the class of all max-injective left R-modules (resp. all max-flat right R-modules).
We prove, in this article, that over a left max-coherent ring every right R-module has an MF-preenvelope, and every left R-module has an MI-cover. Furthermore, it is shown that a ring R is left max-injective if and only if any left R-module has an epic MI-cover if and only if any right R-module has a monic MF-preenvelope. We also give several equivalent characterizations of MI-injectivity and MI-flatness. Finally, MI-dimensions of modules and rings are studied in terms of max-injective modules with the left derived functors of Hom.
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참고문헌 (15)
참고문헌 신청
C. Faith / 1976 / Algebra II, Grundlehren der Mathematischen Wissenschaften, No. 191 / Springer-Verlag
D. J. Fieldhouse / 1969 / Pure theories / Math. Ann. 184 : 1 ~ 18
E. E. Enochs / 1981 / Injective and flat covers, envelopes and resolvents / Israel J. Math. 39 (3) : 189 ~ 209
E. E. Enochs / 2000 / Relative Homological Algebra / Walter de Gruyter & Co.
F. W. Anderson / 1974 / Rings and Categories of Modules, Graduate Texts in Mathematics, Vol. 13 / Springer-Verlag
D. J. Fieldhouse / 1969 / Pure theories / Math. Ann. 184 : 1 ~ 18
E. E. Enochs / 1981 / Injective and flat covers, envelopes and resolvents / Israel J. Math. 39 (3) : 189 ~ 209
E. E. Enochs / 2000 / Relative Homological Algebra / Walter de Gruyter & Co.
F. W. Anderson / 1974 / Rings and Categories of Modules, Graduate Texts in Mathematics, Vol. 13 / Springer-Verlag
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