半环的格林关系所确定的半环簇

doi:10.6040/j.issn.1671-9352.0.2020.453

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (4): 1-7.doi: 10.6040/j.issn.1671-9352.0.2020.453

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半环的格林关系所确定的半环簇

程彦亮,邵勇^*

西北大学数学学院, 陕西西安 710127

发布日期:2021-04-13
作者简介:程彦亮(1996— ),男,硕士研究生,研究方向为半环代数理论. E-mail:2843759341@qq.com*通信作者简介:邵勇(1980— ),男,教授,研究方向为半环代数理论. E-mail:yongshaomath@126.com
基金资助:
国家自然科学基金资助项目(11971383,11801239);陕西省自然科学基金资助项目(2020JM-425)

Semiring varieties defined by Greens relations on a semiring

CHENG Yan-liang, SHAO Yong^*

School of Mathematics, Northwest University, Xian 710127, Shaanxi, China

Published:2021-04-13

摘要/Abstract

摘要： 给出了由半环的格林关系所确定的开同余的刻画与性质。通过这些开同余,得到了系列半环类,证明了这些半环类均是半环簇,并揭示了这些半环簇之间的关系。通过对半环簇的子簇格上的开算子的探究,得到了乘法幂等半环簇的子簇格到开簇格的直积上的序嵌入定理。

关键词: 半环, 格林关系, 开同余, 开算子, 半环簇

Abstract: The properties and characterizations of congruence openings determined by Greens relations of a semiring are given. We obtain that several classes of semirings by means of these congruence openings, prove that these classes of semirings are varieties of semirings, and uncover relationships between these varieties. By exploring opening operators on the lattice of all subvarieties of varieties of semirings, the order embedding theorem of the lattice of all subvarieties of the variety of multiplicatively idempotent semirings into the direct product of the lattice of open varieties is given.

Key words: semiring, Greens relation, congruence opening, opening operator, variety of semirings

中图分类号:

O151.21

程彦亮,邵勇. 半环的格林关系所确定的半环簇[J]. 《山东大学学报(理学版)》, 2021, 56(4): 1-7.

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.

参考文献

[1] 郭聿琦,宫春梅,任学明.关于半群上格林关系的一个来龙去脉的综述[J].山东大学学报(理学版), 2010,45(8):1-18. GUO Yuqi, GONG Chunmei, REN Xueming. A survey on the origin and developments of Greens relations on semigroups[J]. Journal of Shandong University(Natural Science), 2010, 45(8):1-18.
[2] HOWIE J M. Fundamentals of semigroup theory[M] //Algebra Colloquium. London: Clarendon Press, 1995.
[3] ZHAO X Z, SHUM K P, GUO Y Q. L -subvarieties of variety of idempotent semirings[J]. Algebra Universalis, Série I, 2001, 46(1-2):75-96.
[4] ZHAO X Z, GUO Y Q, SHUM K P. D -subvarieties of variety of idempotent semirings[J]. Algebra Colloquium, 2002, 9:15-28.
[5] PASTIJN F. Weak commutativity in idempotent semirings[J]. Semigroup Forum, 2006, 72(2):283-311.
[6] PASTIJN F, GUO Y Q. The lattice of idempotent distributive semirings varieties[J]. Sci China(Ser A), 1999, 42(8):785-804.
[7] PASTIJN F, ROMANOVSKA A. Idempotent distributive semirings I[J]. Acta Sci Math, 1982, 44:239-253
[8] PASTIJN F, ZHAO X Z. Varieties of idempotent semirings with commutative addition[J]. Algebra Universalis, 2005, 54(3):301-321.
[9] SEN M K, GUO Y Q, SHUM K P. A class of idempotent semirings[J]. Semigroup Forum,2000, 60(3):351-367.
[10] WANG Z, ZHOU Y, GUO Y Q. A note on band semirings[J]. Semigroup Forum, 2005, 71(3):439-442.
[11] GRILLET M P. Greens relations in a semiring[J]. Portugaliae Mathematica, 1970, 29(4):181-195.
[12] 秦官伟,任苗苗,邵勇. 关于半环上格林关系的开同余[J].纯粹数学与应用数学, 2012, 28(5):668-675. QIN Guanwei, REN Miaomiao, SHAO Yong. On congruence openings of Greens relations on a semiring[J]. Pure and Applied Mathematics, 2012, 28(5):668-675.
[13] DAMLJANOVIC N, CIRIC M, BOGDANOVIC S. Congruence openings of additive Greens relations on a semigroup[J]. Semigroup Forum, 2011, 82(3):437-454.
[14] CHENG Y L, SHAO Y. Semiring varieties related to multiplicative Greens relations on a semiring[J]. Semigroup Forum, 2020, 101(3):571-584.
[15] FUCHS L. On subdirect unions I[J]. Acta Mathematica Hungarica, 1952, 3:103-120.

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半环的格林关系所确定的半环簇

Semiring varieties defined by Greens relations on a semiring

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