主理想整环上有限生成模之子模与商模之结构 Structure of Submodules and Factors Modules of a Finitely Generated Module over a Principal Ideal Domain

Keywords: 主理想整环,有限生成模,阶理想

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Abstract:

考虑了主理想整环上有限生成模之子模与商模之结构,详细讨论了将模分解成循环子模的直和且循环子模的阶理想满足包含关系时,相应的阶理想与子模或商模相应分解对应的阶理想之间的关系——即前者能控制后者

References

[1]	靳平.有限生成模惟一性定理的新证明[J].武汉大学学报(自然科学版),1986,(4):25-26.Jin P.A new proof of the invariance theorem of the finitely generated module[J].J Wuhan Univ(Nat Sci Ed),1986,(4):25-26(Ch).
[2]	Isaacs I M.Algebra:A Graduate Cause[M].Providence,R I:American Mathematical Society,2009:250-251.
[3]	Artin M.Algebra[M].2nd Edition.San Antonio:Pearson Education,Inc,2011:429-436
[4]	Jacobson N.Basic Algebra I[M].2nd Edition.New York:Dover Publications,2009:189-193.
[5]	王茂福.主理想整环上有限生成模的基本结构定理的另一证明[J].武汉师范学院学报(自然科学版),1982,(2):4-7.Wang M F.Another proof for the fundamental structure thorem for finitely generated modules over a P.I.D[J].J Wuhan Normal Institute(Nat Sci Ed),1982,(2):4-7(Ch).
[6]	Lang S.Algebra[M].Revised Third Edition.Berlin:Springer Sciences+Business Media Inc,2002:146-155.
[7]	喻方元.主理想整环上有限生成模的结构定理的逆定理[J].湖北汽车工业学院学报,2000,14(1):74-75.Yu F Y.The inverse theorem of the fundamental structure theorem for finitely generated modules over a P.I.D[J].J Hubei Automotive Industries Institute,2000,14(1):74-75(Ch).
[8]	王美娟.主理想整环上挠模的元素的阶理想[D].武汉:湖北大学,2010.Wang M J.The Order Ideals of the Elements of a Torsion Module Over PID[D].Wuhan:Hubei University,2010(Ch).

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