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Purities of Ordered Ideals of Ordered Semirings

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주제분류수학

초록

We introduce the concepts of the left purity, right purity, quasi-purity, bipurity, left weak purity and right weak purity of ordered ideals of ordered semirings and use them to characterize regular ordered semirings, left weakly regular ordered semirings, right weakly regular ordered semirings and fully idempotent ordered semirings.

Abstract

We introduce the concepts of the left purity, right purity, quasi-purity, bipurity, left weak purity and right weak purity of ordered ideals of ordered semirings and use them to characterize regular ordered semirings, left weakly regular ordered semirings, right weakly regular ordered semirings and fully idempotent ordered semirings.

참고문헌 (10)

  1. M. R. Adhikari, "Basic modern algebra with applications" (2014), Springer
  2. J. Ahsan, "Pure spectrum of a monoid with zero", Kobe J. Math, 6, pp.163~182 (1989)
  3. Thawhat Changphas, "Pure Ideals in Ordered Semigroups", Kyungpook Mathematical Journal, 54(1), pp.123~129 (2014), 경북대학교 자연과학대학 수학과[DOI]
  4. A. P. Gan, "On ordered ideals in ordered semirings", J. Math. Res. Exposition, 31(6), pp.989~996 (2011)
  5. R. D. Jagatap, "Right k-weakly regular Γ-semirings", Algebra, pp.5~ (2014)
  6. D. Mandal, "Fuzzy ideals and fuzzy interior ideals in ordered semirings", Fuzzy Inf. Eng, 6(1), pp.101~114 (2014)
  7. P. Palakawong na Ayuthaya, "Characterizations of regular ordered semirings by ordered quasi-ideals", Int. J. Math. Math. Sci., pp.8~ (2016)
  8. P. Palakawong na Ayutthaya, "Characterizations of ordered k-regular semirings by ordered quasi k-ideals", Quasigroups Related Systems, 25(1), pp.109~120 (2017)
  9. P. Senarat, "Prime ordered k-bi-ideals in ordered semirings", Quasigroups Related Systems, 25(1), pp.121~132 (2017)
  10. Muhammad Shabir, "One-sided Prime Ideals in Semirings", Kyungpook Mathematical Journal, 47(4), pp.473~480 (2007), 경북대학교 자연과학대학 수학과

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