On Ordered Ideals in Ordered Semirings

被引：0
|
作者：
Ai Ping GAN1
2.Jiangxi Police College
机构：
来源：
Journal of Mathematical Research with Applications | 2011年 / 06期
关键词：
ordered semiring; ordered ideal; simple semiring; minimal ideal; matrix;
D O I：
暂无
中图分类号：
O153.3 [环论];
学科分类号：
070104 ;
摘要：
An ordered semiring is a semiring S equipped with a partial order ≤ such that the operations are monotonic and constant 0 is the least element of S.In this paper,several notions,for example,ordered ideal,minimal ideal,and maximal ideal of an ordered semiring,simple ordered semirings,etc.,are introduced.Some properties of them are given and characterizations for minimal ideals are established.Also,the matrix semiring over an ordered semiring is consid-ered.Partial results obtained in this paper are analogous to the corresponding ones on ordered semigroups,and on the matrix semiring over a semiring.
引用
收藏
页码：989 / 996
页数：8
相关论文
共 50 条
  • [41] ANNIHILATORS AND IDEALS IN ORDERED SETS
    HALAS, R
    [J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 1995, 45 (01) : 127 - 134
  • [42] On Radicals of Ideals of Ordered Semigroups
    Jian TANG1
    2.School of Mathematics and Computational Science
    [J]. Journal of Mathematical Research with Applications, 2010, (06) : 1048 - 1054
  • [43] ON THE ORDERED n-PRIME IDEALS IN ORDERED Gamma-SEMIGROUPS
    Siripitukdet, Manoj
    Iampan, Aiyared
    [J]. COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2008, 23 (01): : 19 - 27
  • [44] Ordered LA-groups and ideals in ordered LA-semigroups
    Kausar, Nasreen
    Munir, Mohammad
    Gulzar, Muhammad
    Alesemi, Meshari
    Salahuddin
    [J]. ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2020, (44): : 723 - 730
  • [45] Characterizing Ordered Bi-Ideals in Ordered F-Semigroups
    Iampan, A.
    [J]. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS, 2009, 4 (01): : 17 - 25
  • [46] Ordered LA-groups and ideals in ordered LA-semigroups
    Kausar, Nasreen
    Munir, Mohammad
    Gulzar, Muhammad
    Alesemi, Meshari
    Salahuddin
    [J]. Italian Journal of Pure and Applied Mathematics, 2020, 44 : 723 - 730
  • [47] CHARACTERIZING THE MINIMALITY AND MAXIMALITY OF ORDERED LATERAL IDEALS IN ORDERED TERNARY SEMIGROUPS
    Iampan, Aiyared
    [J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2009, 46 (04) : 775 - 784
  • [48] CHARACTERIZING ORDERED QUASI-IDEALS OF ORDERED Gamma-SEMIGROUPS
    Iampan, Aiyared
    [J]. KRAGUJEVAC JOURNAL OF MATHEMATICS, 2011, 35 (01): : 13 - 23
  • [49] A note on maximal ideals and prime ideals in ordered semigroups
    Xiao-ping S.
    Wei-qun H.
    [J]. Lobachevskii Journal of Mathematics, 2011, 32 (4) : 317 - 319
  • [50] Roughness Applied to Generalized Γ-ideals of Ordered LA Γ-ideals
    Ansari, Moin Akhtar
    [J]. COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS, 2019, 10 (01): : 71 - 84
12345