Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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REGULARITY AND SEMIPOTENCY OF HOM

  • Hakmi, Hamza (Department of Mathematics Damascus University)
  • Received : 2014.01.18
  • Accepted : 2014.03.25
  • Published : 2014.03.30
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Abstract

Let M, N be modules over a ring R and $[M,N]=Hom_R(M,N)$. 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 questions for 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 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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References

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Cited by

  1. On Fully Idempotent Homomorphisms of Abelian Groups vol.60, pp.4, 2019, https://doi.org/10.1134/s0037446619040189