THE VARIETY OF SEMIRINGS GENERATED BY DISTRIBUTIVE LATTICES AND FINITE FIELDS

被引：3
|
作者：
Shao, Yong [1 ]
Crvenkovic, Sinisa [2 ]
Mitrovic, Melanija [3 ]
机构：
[1] Northwest Univ, Dept Math, Xian, Peoples R China
[2] Univ Novi Sad, Dept Math & Informat, Novi Sad 21000, Serbia
[3] Univ Nis, Fac Mech Engn, Nish, Serbia
来源：
PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD | 2014年 / 95卷 / 109期
基金：
中国博士后科学基金;
关键词：
finite field; distributive lattice; subdirectly irreducible; variety; SUBDIRECT PRODUCTS; PRIMITIVE CLASSES; ARITHMETIC RINGS;
D O I：
10.2298/PIM1409101S
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A semiring variety is d-semisimple if it is generated by the distributive lattice of order two and a finite number of finite fields. A d-semisimple variety V = HSP{B-2,F-1,..., F-k} plays the main role in this paper. It will be proved that it is finitely based, and that, up to isomorphism, the two-element distributive lattice B-2 and all subfields of F-1,... F-k, are the only subdirectly irreducible members in it.
引用
收藏
页码：101 / 109
页数：9
相关论文
共 50 条
  • [1] The Variety of Semirings Generated by Distributive Lattices and Prime Fields
    Yong SHAO
    Miaomiao REN
    JournalofMathematicalResearchwithApplications, 2014, 34 (05) : 529 - 534
  • [2] THE SEMIRING VARIETY GENERATED BY ANY FINITE NUMBER OF FINITE FIELDS AND DISTRIBUTIVE LATTICES
    Shao, Yong
    Ren, Miaomiao
    Crvenkovic, Sinisa
    Mitrovic, Melanija
    PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, 2015, 98 (112): : 45 - 51
  • [3] Varieties of weak lattices covering the variety of distributive lattices
    Fried, Ervin
    ACTA SCIENTIARUM MATHEMATICARUM, 2009, 75 (3-4): : 377 - 392
  • [4] The variety generated by planar modular lattices
    G. Grätzer
    R. W. Quackenbush
    Algebra universalis, 2010, 63 : 187 - 201
  • [5] The variety generated by planar modular lattices
    Graetzer, G.
    Quackenbush, R. W.
    ALGEBRA UNIVERSALIS, 2010, 63 (2-3) : 187 - 201
  • [6] Distributive Lattices of M-Rectangular Divided-semirings
    Shao, Yong
    Zhao, Xianzhong
    ALGEBRA COLLOQUIUM, 2013, 20 (02) : 243 - 250
  • [7] The Structure of Finite Distributive Lattices
    Shmatkov V.D.
    Journal of Mathematical Sciences, 2016, 213 (2) : 276 - 280
  • [8] SMALL REPRESENTATIONS OF FINITE DISTRIBUTIVE LATTICES AS CONGRUENCE LATTICES
    GRATZER, G
    RIVAL, I
    ZAGUIA, N
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 123 (07) : 1959 - 1961
  • [9] Geometric Lattices Generated by Idempotent Matrices over Finite Fields
    Zhang, Ying
    INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS & STATISTICS, 2014, 52 (01): : 52 - 61
  • [10] On (finite) distributive lattices with antitone involutions
    Michal Botur
    Jan Kühr
    Soft Computing, 2014, 18 : 1033 - 1040
12345