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
  • [31] CHARACTERIZATION OF WEAKLY PRIME SUBTRACTIVE IDEALS IN SEMIRINGS
    Gupta, Vishnu
    Chaudhari, J. N.
    [J]. BULLETIN OF THE INSTITUTE OF MATHEMATICS ACADEMIA SINICA NEW SERIES, 2008, 3 (02): : 347 - 352
  • [32] One-sided Prime Ideals in Semirings
    Shabir, Muhammad
    Iqbal, Muhammad Sohail
    [J]. KYUNGPOOK MATHEMATICAL JOURNAL, 2007, 47 (04): : 473 - 480
  • [33] Prime congruences of additively idempotent semirings and a Nullstellensatz for tropical polynomials
    Dániel Joó
    Kalina Mincheva
    [J]. Selecta Mathematica, 2018, 24 : 2207 - 2233
  • [34] Prime congruences of additively idempotent semirings and a Nullstellensatz for tropical polynomials
    Joo, Daniel
    Mincheva, Kalina
    [J]. SELECTA MATHEMATICA-NEW SERIES, 2018, 24 (03): : 2207 - 2233
  • [35] On Prime, Weakly Prime Left Ideals and Weakly Regular Ternary Semirings
    Bhambri, S. K.
    Dubey, Manish Kant
    Anuradha
    [J]. SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2013, 37 (06) : 801 - 811
  • [36] Factor rank preservers of matrices over additively-idempotent multiplicatively-cancellative semirings
    Maity, Sushobhan
    Bhuniya, A. K.
    [J]. ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2021, 14 (05)
  • [37] On Rings Whose Strongly Prime Ideals Are Completely Prime
    Huh, Chan
    Lee, Chang Ik
    Lee, Yang
    [J]. ALGEBRA COLLOQUIUM, 2010, 17 (02) : 283 - 294
  • [38] ON WEAKLY COMPLETELY QUASI PRIMARY AND COMPLETELY QUASI PRIMARY IDEALS IN TERNARY SEMIRINGS
    Yiarayong, Pairote
    [J]. COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2016, 31 (04): : 657 - 665
  • [39] COMPLETELY PRIME IDEALS AND IDEMPOTENTS IN MOBS
    SHUM, KP
    STEWART, PN
    [J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 1976, 26 (02) : 211 - 217
  • [40] Prime bi-ideals in ordered ternary semirings
    Elavarasan, B.
    Porselvi, K.
    [J]. INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2019, 14 (04): : 929 - 933
12345