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χ-quasi-continuous mode

L, M1nK = 0. Let: M a natural projection,[link widoczny dla zalogowanych], then lx is a monomorphism, so K Lan 7r (K) and Ko = o7r (K). Because it is closed on the sub-module module class, so n ∈ () and 7r (K) ∈ (M2). Because it is weak type 1 ZC model, so there is N, Ⅳ】 make-NoN and N is the complement of n in that (n) nN = 0, (n) oN ≤. There are also N,[link widoczny dla zalogowanych], Ⅳ 2, so = N0 Ⅳ 2 and N is a 7r (K) in the supplement, that is, 7r (K) nN2 = 0,7 r (K) oN ≤. Obviously NoNc0,[link widoczny dla zalogowanych], so by [7,1.5 (7)] to know, (n) oNoK ≤, oK = o7r (K). Also by [7,1.5 (7)] to know, (n) oNoKoN2 ≤, M1o7r (K) oN ≤ M10M2. By [7,1.5 (2)] know that (n) oNoKoN ≤ o. And because (n) oK ≤, L, so n (NoN) 10, so oNoN ≤ o. By [3,[link widoczny dla zalogowanych], Lemma 2.2] the known NoN is the complement of M, it is a weak type 1 ZC mode. Thanks: sincerely thank the teachers and Huan Xie Chenmiao Sen Gen teacher guidance and help. 【Reference】 IllMOHAMEDSH, MULLERBJ. Continuousanddiscretemodules [M]. LondonMathSocLectureNoteSer147, London: CambridgeUniversityPress, 1990. [2] SANTA-CLARAc, ITHPF. Extendingmoduleswhicharedirectsumofinjectivemodulesandsemisimplemodules [J]. CommAlgebra, 1996,24:364 l ~ 3651. [3] ITHPF, TERCANA. GeneralizationsofCS-modules mouth]. CommAlgebra, 1993,29: l809-1847. [4] ITHPF. CS-modulesandweakCS-modules [M]. inLectureNotesinMath1448, Springer-Vertag, 1990. [5] DOGROZS,[link widoczny dla zalogowanych], ITHPF. Moduleswhichareextendingrelationtomodulesclasses [J]. Comm. Algebra, 1998,26: l699 a l721. [6] Yang Shizhou. I-I-a continuous mode and a quasi-continuous mode port]. Lanzhou University, 2002,38 (4): l7-21. [7] DUNGNV, HUYNHDV, ITHPF, eta1. Extendingmodules [M]. PitmanResNotesMathSer313, 1994. [8] DOGRUOZS. SmithPF. Moduleswhichareweakex-tendingrelationtomodulesclasses [J]. ActaMathHun-gar, 2000,87 (1 ~ 2) t1 ~ 10. Citation reference to the motive of scientific literature and cited that the content of scientific knowledge and information and use of inheritance, but motivations cited by scholars Weinstock (M. Weinstock) study. Citation has the following 15 kinds of motives: (1) to pay tribute to the pioneers; (2) to give honor to the relevant works; (3) verification methods and instruments they use; (4) provides background reading; (5) own writings to be corrected; (6) work for others to be corrected; (7) to evaluate the previous work; o ●:: lul o ●: '. o ● o ●: '. o ●: '. ( Cool

for their own ideas to seek the full argument; (9) to provide researchers the existing work; (1O) for not spread or not indexing is rarely cited literature guides; (11) to verify data and physical constants; (12) to check the original data on an idea or concept is being discussed; (13) to check the original data, or other writings in the cause of a concept or term character; (14) acknowledged master of others Lake group concept; (15) to dispute priority claims of others.

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