Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A GENERALIZATION OF INSERTION-OF-FACTORS-PROPERTY

  • Published : 2007.02.28
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Abstract

We in this note introduce the concept of g-IFP rings which is a generalization of IFP rings. We show that from any IFP ring there can be constructed a right g-IFP ring but not IFP. We also study the basic properties of right g-IFP rings, constructing suitable examples to the situations raised naturally in the process.

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References

  1. H. E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc. 2 (1970), 363-368 https://doi.org/10.1017/S0004972700042052
  2. G. F. Birkenmeier, H. E. Heatherly, and E. K. Lee, Completely prime ideals and as-sociated radicals, Proc. Biennial Ohio State-Denison Conference 1992, edited by S. K. Jain and S. T. Rizvi, World Scientific, Singapore-New Jersey-London-Hong Kong (1993), 102-129
  3. K. R. Goodearl, von Neumann Regular Rings, Pitman, London, 1979 https://doi.org/10.1090/S0273-0979-1980-14812-0
  4. J. M. Habeb, A note on zero commutative and duo rings, Math. J. Okayama Univ. 32 (1990), 73-76
  5. Y. Hirano, Some studies on strongly $\pi$-regular rings, Math. J. Okayama Univ. 20 (1978), no. 2, 141-149
  6. N. K. Kim and Y. Lee, Extensions of reversible rings, J. Pure Appl. Algebra 185 (2003), no. 1-3, 207-223 https://doi.org/10.1016/S0022-4049(03)00109-9
  7. J. Lambek, Lectures on Rings and Modules, Blaisdell, Waltham, 1966
  8. Y. Lee, H. K. Kim, and C. Huh, Questions on 2-primal rings, Comm. Algebra 26 (1998), no. 2, 595-600 https://doi.org/10.1080/00927879808826150
  9. G. Marks, Direct product and power series formations over 2-primal rings, in (eds. S. K. Jain, S. T. Rizvi) Advances in Ring Theory, Trends in Math., Birkhauser, Boston (1997), 239-245
  10. L. Motais de Narbonne, Anneaux semi-commutatifs et uniseriels; anneaux dont les ideaux principaux sont idempotents, In: Proceedings of the 106th National Congress of Learned Societies (Perpignan, 1981), Bib. Nat., Paris (1982), 71-73
  11. G. Shin, Prime ideals and sheaf representation of a pseudo symmetric ring, Trans. Amer. Math. Soc. 184 (1973), 43-60 https://doi.org/10.2307/1996398

Cited by

  1. On a Class of Semicommutative Rings vol.51, pp.3, 2011, https://doi.org/10.5666/KMJ.2011.51.3.283