The Extension of MT Ideals and the Existence of Prime MT Ideal in BR<sub>0</sub>-Algebras

WU Hong-bo; WANG Na

doi:10.3969/j.issn.0372-2112.2015.06.015

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The Extension of MT Ideals and the Existence of Prime MT Ideal in BR₀-Algebras

更新时间：2025-07-16

- The Extension of MT Ideals and the Existence of Prime MT Ideal in BR₀-Algebras
- Acta Electronica Sinica Vol. 43, Issue 6, Pages: 1137-1143(2015)
- 作者机构：
  
  陕西师范大学数学与信息科学学院,陕西,西安,710062
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.11171196);Fundamental Research Funds for the Central Universities (No.GK201501001)
- DOI：10.3969/j.issn.0372-2112.2015.06.015
  CLC： O141.1
- Published：2015
- 稿件说明：
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WU Hong-bo, WANG Na. The Extension of MT Ideals and the Existence of Prime MT Ideal in BR₀-Algebras[J]. Acta Electronica Sinica, 2015, 43(6): 1137-1143.
DOI：

WU Hong-bo, WANG Na. The Extension of MT Ideals and the Existence of Prime MT Ideal in BR₀-Algebras[J]. Acta Electronica Sinica, 2015, 43(6): 1137-1143. DOI： 10.3969/j.issn.0372-2112.2015.06.015.

摘要

-代数是一类重要的基础逻辑代数

其中著名的MV代数和R

-代数均是BR

-代数的特款

因而对BR

-代数研究结果具有普遍的实用性.首先

通过BR

-代数中极大并-理想的存在性证明了BR

-代数中素并-理想的存在性;其次

利用对偶范畴的思想方法和MP滤子的特征

在BR

-代数中提出了MT理想

极大MT理想

素MT理想等概念

讨论了它们的基本性质及相互关系

并通过素并-理想构造性的证明了素MT理想的存在性;最后

在非退化的BR

-代数中证明了任何一个真MT理想可以扩展为一个极大素MT理想.本文的工作是对BR

-代数研究内容和方法的有益补充.

Abstract

-algebras are important basic algebras

which take MV algebras and R

-algebras as their exceptions

so the study results of BR

-algebras have universal applicability.Firstly

the existence of prime union-ideals is proved through the existence of maximal union-ideals in BR

-algebras;Secondly

having utilized the ideals and methods of dual category and characteristic of MP filter

the concepts of MT ideal

maximal MT ideal

prime MT ideal are introduced to BR

-algebras

and the relationships among them are discussed

and the existence of prime MT ideal

s is proved by constructing of prime MT ideals through prime union-ideals in BR

-algebras;At last

it is proved that a proper MT ideal can be expended to a maximal prime MT ideal.The work of the paper is a beneficial supplement for the content and methods of studying series BR

-algebras.

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The Extension of MT Ideals and the Existence of Prime MT Ideal in BR0-Algebras

DOI：10.3969/j.issn.0372-2112.2015.06.015

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The Extension of MT Ideals and the Existence of Prime MT Ideal in BR₀-Algebras