DISTRIBUTIVE LATTICES OF JACOBSON RINGS

被引：0
作者：
Shao, Yong [1 ]
Crvenkovic, Sinisa [2 ]
Mitrovic, Melanija [3 ]
机构：
[1] Northwest Univ, Sch Math, Xian, Peoples R China
[2] Univ Novi Sad, Dept Math & Informat, Novi Sad, Serbia
[3] Univ Nis, Fac Mech Engn, Nish, Serbia
来源：
PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD | 2016年 / 100卷 / 114期
关键词：
semiring; distributive lattice; Jacobson ring; Mal'cev product; congruence;
D O I：
10.2298/PIM1614087S
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We characterize the distributive lattices of Jacobson rings and prove that if a semiring is a distributive lattice of Jacobson rings, then, up to isomorphism, it is equal to the subdirect product of a distributive lattice and a Jacobson ring. Also, we give a general method to construct distributive lattices of Jacobson rings.
引用
收藏
页码：87 / 93
页数：7
相关论文
共 11 条
[1]   SUBDIRECT PRODUCTS OF RINGS AND DISTRIBUTIVE LATTICES [J].
BANDELT, HJ ;
PETRICH, M .
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1982, 25 (JUN) :155-171
[2]  
Galbiati J. L., 1980, REND SCI MAT APPL A, V114, P73
[3]   A characterization of semirings which are subdirect products of a distributive lattice and a ring [J].
Ghosh, S .
SEMIGROUP FORUM, 1999, 59 (01) :106-120
[4]   The semigroup structure of left Clifford semirings [J].
Guo, YQ ;
Shum, KP ;
Sen, MK .
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2003, 19 (04) :783-792
[5]  
Howie J.M., 1995, FUNDAMENTALS SEMIGRO
[6]   STRUCTURE THEORY FOR ALGEBRAIC ALGEBRAS OF BOUNDED DEGREE [J].
JACOBSON, N .
ANNALS OF MATHEMATICS, 1945, 46 (04) :695-707
[7]  
Pastijn F, 2002, SCI CHINA SER A, V45, P172
[8]  
Petrich M., 1999, CAN MATH SOC SER MON
[9]   THE VARIETY OF SEMIRINGS GENERATED BY DISTRIBUTIVE LATTICES AND FINITE FIELDS [J].
Shao, Yong ;
Crvenkovic, Sinisa ;
Mitrovic, Melanija .
PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, 2014, 95 (109) :101-109
[10]   Distributive Lattices of M-Rectangular Divided-semirings [J].
Shao, Yong ;
Zhao, Xianzhong .
ALGEBRA COLLOQUIUM, 2013, 20 (02) :243-250
12