대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제61권3호
  • /
  • Pages.797-811
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  • 2024
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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A TORSION GRAPH DETERMINED BY EQUIVALENCE CLASSES OF TORSION ELEMENTS AND ASSOCIATED PRIME IDEALS

  • Reza Nekooei (Department of Pure Mathematics Mahani Mathematical Research Center Shahid Bahonar University of Kerman) ;
  • Zahra Pourshafiey (Department of Pure Mathematics Mahani Mathematical Research Center Shahid Bahonar University of Kerman)
  • 투고 : 2023.07.12
  • 심사 : 2023.11.03
  • 발행 : 2024.05.31
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초록

In this paper, we define the torsion graph determined by equivalence classes of torsion elements and denote it by AE(M). The vertex set of AE(M) is the set of equivalence classes {[x] | x ∈ T(M)*}, where two torsion elements x, y ∈ T(M)* are equivalent if ann(x) = ann(y). Also, two distinct classes [x] and [y] are adjacent in AE(M), provided that ann(x)ann(y)M = 0. We shall prove that for every torsion finitely generated module M over a Dedekind domain R, a vertex of AE(M) has degree two if and only if it is an associated prime of M.

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참고문헌

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