Quasi-Splitting Exact Sequence

Hou, Hsiang-Dah

Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 503-506

Résumé

Let R be a ring with 1 ≠ 0 and α, β, γ R-endomorphisms of R-modules A, B, and C respectively. We shall denote by M(R) the category of R-modules, and by End(R) the category of R-endomorphisms. For objects α and β of End(R) a morphism λ: α → β is an R-homomorphism such that λα = β λ. We shall denote by Idm(R) the full subcategory of End(R) whose objects are idempotents. Idm(R) is an abelian category, ker, coker and im are constructed in the naive way and hence is exact in M(R) if and only if is exact in Idm(R), where the domains of α,β, and γ are A, B, and C respectively. One sees that End (R) as well as Idm(R) is abelian.

Détail

DOI : 10.4153/CJM-1971-053-9

Bibliographie

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