JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (11): 65-69.doi: 10.6040/j.issn.1671-9352.0.2023.429

Previous Articles    

Full congruences of a semiring variety

TAO Binghui, SHAO Yong*   

  1. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China
  • Published:2025-11-11

PDF (PC)

41

Abstract: The definitions of full equivalence relations and full congruences of a semiring variety are introduecd. A method of generating a full congruence with an arbitrary full equivalence relation is presented. Several varieties of semirings defined by full congruences are characterized and described. Some connections between these semring varieties are given and discussed. The results obtained generalize the relevant conclusions.

Key words: semiring, congruence, variety, homomorphic image, subdirect product

CLC Number: 

  • O153.5
[1] BURRIS S, SANKAPPANAVAR H P. A course in universal algebra[M]. New York: Springer, 1981.
[2] PASTIJN F. Idempotent distributive semirings II[J]. Semigroup Forum, 1983, 26(1):151-166.
[3] HOWIE J M. Fundamentals of semigroup theory[M]. New York: Oxford University Press, 1995.
[4] 赵宪钟,邵勇,任苗苗. 中国半环理论研究综述[J]. 数学进展,2022,51(5):781-795. ZHAO Xianzhong, SHAO Yong, REN Miaomiao. A survey on the study of semiring theory in China[J]. Advance In Mathematics, 2022, 51(5):781-795.
[5] PASTIJN F, ZHAO X Z. Greens D -relation for the multiplicative reduct of an idempotent semiring[J]. Archivum Mathematicum, 2000, 36(2):77-93.
[6] ZHAO X Z, GUO Y Q, SHUM K P. D -subvarieties of the variety of idempotent semirings[J]. Algebra Colloquium, 2002, 9(1):15-28.
[7] ZHAO X Z, SHUM K P, GUO Y Q. L-subvarieties of idempotent semirings[J]. Algebra Universalis, 2001, 46(1/2):75-96.
[8] DAMLJANOVIC N, CIRIC M, BOGDANOVIC S. Congruence openings of additive Greens relations on a semiring[J]. Semigroup Forum, 2011, 82(3):437-454.
[9] CHENG Yanliang, SHAO Yong. Semiring varieties related to multiplicative Greens relations on a semiring[J]. Semigroup Forum, 2020, 101(3):571-584.
[10] XIAN X L, SHAO Y, CRVENKOVIC S. Semiring varieties related to closure congruences of Greens relations[J]. Publicationes Mathematicae Debrecen, 2023, 102(3/4):401-413.
[11] VECHTOMOV E M, PETROV A A. Multiplicatively idempotent semirings[J]. Journal of Mathematical Sciences, 2015, 206(6):634-653.
[12] BIRKHOFF G. Subdirect unions in universal algebra[J]. Bulletin of the American Mathematical, 1944, 50:764-768.
[13] FUCHS L. On subdirect unions I[J]. Acta Mathematica Hungarica, 1952, 3:103-120.
[1] YANG Jizhen, WANG Yunpeng. Some super congruences involving Catalan numbers [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(5): 93-99.
[2] LIU Ni, CUI Panpan. On the properties of S-hyperlattice ideals [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(2): 1-8.
[3] WU Yanan. The additively idempotent semiring variety V(S(a2b)) [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(11): 59-64.
[4] Jing TIAN,Jiahao GONG. Combinatorial properties and algebraic characterization of the strict mono-affix languages [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(6): 91-97, 107.
[5] Chunmei GONG,Jiao PENG,Xuena bai. Good congruences on r-wide semigroups whose idempotents form normal band [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(6): 6-12.
[6] Yuchen FU,Yong SHAO. Some subvarieties of semiring variety COSn· [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(4): 31-37.
[7] SHAO Lei, GONG Chunmei. Several classes of good congruences on r-wide semigroups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(12): 46-53.
[8] WU Haigang, GAO Baijun. The number of endomorphisms and automorphisms of a class of non-abelian groups with order 8p [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(12): 60-65.
[9] LI Chun-hua, MENG Ling-xiang, FANG Jie-ying. Congruences on type B semigroups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(2): 20-27.
[10] WANG Jun-ling, SHAO Yong. Greens relations on a class of semiring which multiplicative reduct is an idempotent semigroup [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(6): 15-22.
[11] WANG Jing, GONG Chun-mei. Tropical matrix semigroups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(2): 50-55.
[12] CUI Qian, GONG Chun-mei, WANG Hui. (~)-Good congruences on Rees matrix semigroups over semiadequate semigroups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(2): 61-66.
[13] DENG Wei-na, ZHAO Xian-zhong. Linear operators preserving transitive closures of matrices over the binary Boolean semiring [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(12): 64-70.
[14] WEI Meng-jun, LI Gang. The property and structure of left Clifford bi-semirings [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(8): 45-48.
[15] CHENG Yan-liang, SHAO Yong. Semiring varieties defined by Greens relations on a semiring [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(4): 1-7.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd