논문KCI 등재
Characterizations of ordered intra $k$-regular semirings by ordered $k$-ideals
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
We introduce the notion of ordered intra $k$-regular semirings, characterize them using their ordered $k$-ideals and prove that an ordered semiring $S$ is both ordered $k$-regular and ordered intra $k$-regular if and only if every ordered quasi $k$-ideal or every ordered $k$-bi-ideal of $S$ is ordered $k$-idempotent.
Abstract
We introduce the notion of ordered intra $k$-regular semirings, characterize them using their ordered $k$-ideals and prove that an ordered semiring $S$ is both ordered $k$-regular and ordered intra $k$-regular if and only if every ordered quasi $k$-ideal or every ordered $k$-bi-ideal of $S$ is ordered $k$-idempotent.
참고문헌 (14)
- M. R. Adhikari, "On k-regular semirings", Bull. Calcutta Math. Soc., 88(2), pp.141~144 (1996)
- J. Ahsan, "Fuzzy semirings with applications to automata theory, Studies in Fuzziness and Soft Computing", pp.278~ (2012), Springer
- A. K. Bhuniya, "Bi-ideals in k-regular and intra k-regular semirings", Discuss. Math. Gen. Algebra Appl., 31(1), pp.5~25 (2011)[DOI]
- S. Bourne, "The Jacobson radical of a semiring", Proc. Nat. Acad. Sci. U.S.A., 37(3), pp.163~170 (1951)[DOI]
- A. P. Gan, "On ordered ideals in ordered semirings", J. Math. Res. Exposition, 31(6), pp.989~996 (2011)
- K. Jana, "Quasi k-ideals in k-regular and intra k-regular semirings", Pure Math. Appl. (PU.M.A.), 22(1), pp.65~74 (2011)
- S. Lajos, "A note on intra-regular semigroups", Proc. Japan Acad., 39, pp.626~627 (1963)
- D. Mandal, "Fuzzy ideals and fuzzy interior ideals in ordered semirings", Fuzzy Inf. Eng., 6(1), pp.101~114 (2014)[DOI]
- P. Palakawong na Ayutthaya, "Characterizations of regular ordered semirings by ordered quasi-ideals", Int. J. Math. Math. Sci., pp.8~ (2016)
- P. Palakawong na Ayutthaya, "Characterizations of intra-regular ordered semirings by ordered quasi-ideals", Proceeding of The National and International Graduate Research Conference, pp.102~109 (2016), Graduate School, Khon Kaen University
- P. Palakawong na Ayutthaya, "Characterizations of ordered k-regular semirings by ordered quasi k-ideals", Quasigroups Related Systems, 25(1), pp.109~120 (2017)
- S. Patchakhieo, "Characterizations of ordered k-regular semirings by ordered k-ideals", Asian-Eur. J. Math., 10(2), pp.1750020~1750033 (2017)[DOI]
- P. Senarat, "Prime ordered k-bi-ideals in ordered semirings", Quasi-groups Related Systems, 25(1), pp.121~132 (2017)
- M. Shabir, "A note on quasi-ideals in semirings", Southeast Asian Bull. Math., 27(5), pp.923~928 (2004)
관련 논문AI추천
Purities of Ordered Ideals of Ordered SemiringsBundit Pibaljommee, Pakorn Palakawong na Ayutthaya경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2020 · 제60권 제3호Intra-regular and weakly regular ordered ternary semigroupsShahida Bashir, Xiankun Du기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2017 · 제13권 제4호On Ordered Ternary SemigroupsVanita Rohit Daddi, Yashashree Shivajirao Pawar경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2012 · 제52권 제4호Generalized ideal elements in le-Γ-semigroupsEdmond Pisha, Kostaq Hila대한수학회 · 대한수학회논문집2011 · 제26권 제3호T-fuzzy ideals in ordered Γ-semiringsMarapureddy Murali Krishna Rao기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2017 · 제13권 제2호Characterization of regular semigroup by (∈, ∈∨(k*, q_k))-fuzzy idealsKhaista Rahman, Muhammad Sajjad Ali Khan, Saleem Abdullah, Syed Zaheer Abbas기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2017 · 제13권 제3호
이 간행물의 다른 논문 (26건)
Explicit evaluation of harmonic sumsCe Xupp. 13-36Commutativity of Jordan ideals in 3-prime near-rings with derivationsAbdelkarim Bouapp. 37-44Some remarks on Camillo-Krause conjectureBahram Amirsardaripp. 45-51Two descriptions of relative derived categoriesPayam Bahiraeipp. 53-71Remarks on generalized Jordan $(\alpha, \beta)^\ast$-derivations of semiprime rings with involutionMotoshi Hongan, Nadeem Ur Rehmanpp. 73-83