A note on the number of subquantales

被引：0

作者：

Shengwei Han

Bin Zhao

Shunqin Wang

机构：

[1] Shaanxi Normal University,Department of Mathematics

[2] Nanyang Normal University,School of Mathematics and Statistics

来源：

Algebra universalis | 2013年 / 69卷

关键词：

06F07; quantale; simple quantale; quantic conucleus; subquantale;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this note, it is proved for n ≤ 5 that if Q is a finite quantale with |Q| ≥ n, then there are at least n subquantales of Q. However, the result does not hold when |Q| ≥ 6. Also, an example is given of a sequence of quantales of cardinality p + 2 for p prime, each of which have exactly 5 subquantales.

引用

页码：191 / 200

页数：9

共 12 条

[1]

Han S.-W.(2009)The quantic conuclei on quantales Algebra Universalis 61 97-114

[2]

Zhao B.(1986)Rend Circ. Mat Palermo (2) Suppl 12 99-104

[3]

Mulvey C.J.(2007)Ideal and congruence on quantale Journal of Chongqing University (Natural Science Edition) 30 89-94

[4]

Pan F.-F.(2000)Embeddings of quantales into simple quantales J. Pure Appl. Algebra 148 209-216

[5]

Han S.-W.(1997)Simple involutive quantales J. Algebra 195 367-386

[6]

Paseka J.(2008)On the category Q-Mod Algebra Universalis 58 35-58

[7]

Kruml D.(2003)Ideal of quantale Journal of Shaanxi Normal University (Natural Science Edition) 31 7-10

[8]

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[9]

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