10.1186/2251-7456-6-70

Graded coprime submodules

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  • Rezvan Varmazyar*1,
  1. Department of Mathematics, Islamic Azad University Khoy Branch, Khoy, 58168-44799, IR

Published in Issue 2012-12-10

How to Cite

Varmazyar, R. (2012). Graded coprime submodules. Mathematical Sciences, 6(1). https://doi.org/10.1186/2251-7456-6-70
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Abstract

Abstract Abstract Let G be a group. Let R be a G -graded commutative ring with identity, and let M be a G -graded module over R . Two graded submodules N and K of graded module M are called graded coprime whenever N  +  K  =  M . In this paper, some properties of graded coprime submodules are discussed. For example, we show that if M is a graded finitely generated module, then two graded submodules N and K of M are graded coprime if and only if grad M ( N ) and grad M ( K ) are graded coprime.

Keywords

  • Graded multiplication module,
  • Graded coprime submodule,
  • Graded cancelation module,
  • 13A02; 16W50
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References

  1. Atani (2010) Graded modules which satisfy the Gr-radical formula 8(1) (pp. 161-170)
  2. Oral et al. (2010) On graded prime and primary submodules (pp. 1-9)
  3. Atiyah and Macdonald (1969) Addison-Wesley
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  5. El-Bast and Smith (1988) Multiplication modules 16(4) (pp. 755-779) https://doi.org/10.1080/00927878808823601
  6. Ameri (2003) On the prime submodules of multiplication modules 2003(27) (pp. 1715-1724) https://doi.org/10.1155/S0161171203202180
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