Completely Prime Ideals in Multiplicatively Idempotent Semirings

被引：2
|
作者：
Vechtomov, E. M. [1 ]
Petrov, A. A. [1 ]
机构：
[1] Vyatka State Univ, Kirov 610000, Russia
来源：
MATHEMATICAL NOTES | 2022年 / 111卷 / 3-4期
关键词：
semiring; multiplicatively idempotent semiring; completely prime ideal; maximal ideal; commutativity; Boolean ring; generalized Boolean lattice;
D O I：
10.1134/S0001434622030191
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Structure properties of multiplicatively idempotent semirings are considered. Basic results concerning completely prime ideals in multiplicatively idempotent semirings are obtained. The main theorem describes the commutative multiplicatively idempotent semirings with zero in which all completely prime ideals are maximal: up to isomorphism, such semirings are exhausted by direct products of a Boolean ring and a generalized Boolean lattice. Examples are given showing that the conditions of commutativity and the presence of zero are essential.
引用
收藏
页码：515 / 524
页数：10
相关论文
共 50 条
  • [41] A NOTE ON PRIME QUASI-IDEALS IN TERNARY SEMIRINGS
    Dubey, Manish Kant
    Anuradha
    [J]. KRAGUJEVAC JOURNAL OF MATHEMATICS, 2013, 37 (02): : 361 - 367
  • [42] COMPLETELY PRIME IDEALS IN ORE EXTENSIONS
    LORENZ, M
    [J]. COMMUNICATIONS IN ALGEBRA, 1981, 9 (11) : 1227 - 1232
  • [43] Various Generalized Prime Fuzzy Ideals of Semirings.
    Mohanraj, G.
    Azhaguvelavan, S.
    [J]. 11TH NATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS, 2019, 2112
  • [44] 1-(2-) Prime Ideals in Semirings
    Nandakumar, Pandarinathan
    [J]. KYUNGPOOK MATHEMATICAL JOURNAL, 2010, 50 (01): : 117 - 122
  • [45] Prime one-sided ideals in ternary semirings
    Luangchaisri, Panuwat
    Changphas, Thawhat
    [J]. INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2024, 19 (02): : 403 - 409
  • [46] WEAKLY PRIME AND WEAKLY COMPLETELY PRIME IDEALS OF NONCOMMUTATIVE RINGS
    Groenewald, Nico
    [J]. INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA, 2020, 28 : 43 - 60
  • [47] 2 NOTES ON MULTIPLICATIVELY CLOSED-SETS OF IDEALS AND PRIME DIVISORS
    MIRBAGHERI, A
    RATLIFF, LJ
    [J]. COMMUNICATIONS IN ALGEBRA, 1990, 18 (03) : 863 - 871
  • [48] k-prime and k-semiprime ideals of semirings
    Purkait, S.
    Dutta, T. K.
    Kar, S.
    [J]. ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2021, 14 (03)
  • [49] A NOTE ON COMPLETELY PRIME IDEALS OF ORE EXTENSIONS
    Bhat, V. K.
    [J]. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2010, 20 (03) : 457 - 463
  • [50] On Completely Prime Left Ideals of Ore Extensions
    Bhat, V. K.
    [J]. LOBACHEVSKII JOURNAL OF MATHEMATICS, 2015, 36 (01) : 79 - 84
12345