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Let M, N be modules over a ring R and [M,N]= text Hom_R(M,N). The concern is study of: (1) Some fundamental properties of [M,N] when [M,N] is regular or semipotent. (2) The substructures of [M,N] such as radical, the singular and co-singular ideals, the total and others has raised new questionsfor research in this area. New results obtained include necessary and sufficient conditions for [M,N] to be regular or semipotent. New substructures of [M,N] are studied and its relationship with the text Tot of [M,N]. In this paper we show that, the endomorphism ring of a module M is regular if and only if the module M is semi-injective (projective) and the kernel (image) of every endomorphism is a direct summand.
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참고문헌 (9)
참고문헌 신청
F. Kasch / 1982 / Modules and Rings / Academic Press
F. Kasch / 2002 / Locally injective and locally projective modules / Rocky Mountain J. Math 32 (4) : 1493 ~ 1504
F. Kasch / 2004 / Rings, Modules, and the Total, Front. Math. / Birkhauser Verlag
F. Kasch / 2008 / Regular Substructures of Hom / Appl. Categ. Structures 16 : 159 ~ 166
G.M. Tsukerman / 1966 / Rings of endomorphisms of free modules / Sibirsk. Mat. Zh 7 (7) : 1161 ~ 1167
F. Kasch / 2002 / Locally injective and locally projective modules / Rocky Mountain J. Math 32 (4) : 1493 ~ 1504
F. Kasch / 2004 / Rings, Modules, and the Total, Front. Math. / Birkhauser Verlag
F. Kasch / 2008 / Regular Substructures of Hom / Appl. Categ. Structures 16 : 159 ~ 166
G.M. Tsukerman / 1966 / Rings of endomorphisms of free modules / Sibirsk. Mat. Zh 7 (7) : 1161 ~ 1167
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