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- W804525287 abstract "For any S−flat module RM(which will be called endo- flat) with a commutative ring R with identity, where S is the endomor- phism ring RM, the fact that every epimorphism is an automorphism has been proved and the Jacobson Radical Rad(S )o fS is described as follows; Rad(S )= { f ∈ S | Imf = Mf is small in M } = { f ∈ S | Imf ≤ Rad(M) }. Additionally for any quasi-injective endo-flat module RM, the fact that every monomorphism is an au- tomorphism has been proved and the Jacobson Radical Rad(S )f or any quasi-injective endo-flat module has been studied too. Also some equivalent conditions for the semi-primitivity of any faithful endo-flat module RM with the open Jacobson Radical Rad(M) and those for the semi-simplicity of of any faithful endo-flat quasi-injective module RM with the closed Socle Soc(M) have been studied." @default.
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- W804525287 date "2000-01-01" @default.
- W804525287 modified "2023-09-23" @default.
- W804525287 title "THE JACOBSON RADICAL OF THE ENDOMORPHISM RING, THE JACOBSON RADICAL, AND THE SOCLE OF AN ENDO-FLAT MODULE" @default.
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