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电子学报  2015 

BR0-代数中MT理想的扩展及素MT理想的存在性

DOI: 10.3969/j.issn.0372-2112.2015.06.015, PP. 1137-1143

Keywords: 逻辑代数,BR0-代数,素并-理想,MT理想,扩展,素MT理想,存在性

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Abstract:

BR0-代数是一类重要的基础逻辑代数,其中著名的MV代数和R0-代数均是BR0-代数的特款,因而对BR0-代数研究结果具有普遍的实用性.首先,通过BR0-代数中极大并-理想的存在性证明了BR0-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BR0-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BR0-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BR0-代数研究内容和方法的有益补充.

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