Algebraic and topological results on lifting properties in residuated lattices

Georgescu George; Cheptea Daniela; Muresan Claudia

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Algebraic and topological results on lifting properties in residuated lattices

机译：剩余格中提升性质的代数和拓扑结果

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摘要

We define lifting properties for universal algebras, which we study in this general context and then particularize to various such properties in certain classes of algebras. Next we focus on residuated lattices, in which we investigate lifting properties for Boolean and idempotent elements modulo arbitrary, as well as specific kinds of filters. We give topological characterizations to the lifting property for Boolean elements and several properties related to it, many of which we obtain by means of the reticulation. (C) 2014 Elsevier B.V. All rights reserved.

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来源
《Fuzzy sets and systems》 |2015年第15期|102-132|共31页
作者
Georgescu George; Cheptea Daniela; Muresan Claudia;
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作者单位

Univ Bucharest, Fac Math & Comp Sci, Acad 14, RO-010014 Bucharest, Romania;

Univ Bucharest, Fac Math & Comp Sci, Acad 14, RO-010014 Bucharest, Romania;

Univ Bucharest, Fac Math & Comp Sci, Acad 14, RO-010014 Bucharest, Romania;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Universal algebra; (Local, semilocal, maximal, hyperarchimedean, simple, semisimple) residuated lattice; Lifting Property; (Prime, maximal) spectrum; Stone topology; Reticulation;

机译：通用代数;（局部;半局部;最大;超体系结构;简单;半简单）剩余格;提升性质;（素数;最大）频谱;石拓扑;网状结构;

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1. Boolean lifting property for residuated lattices [J] . George Georgescu, Claudia Mure?an Soft computing: A fusion of foundations, methodologies and applications . 2014,第11期

机译：剩余格的布尔提升特性
2. Residuated EQ-algebras may not be residuated lattices [J] . Fuzzy sets and systems . 2020,第Mara1期

机译：剩余的EQ代数可能不是剩余的点阵
3. The finite embeddability property for residuated lattices, pocrims and BCK-algebras [J] . W. J. Blok, C. J. van Alten Algebra Universalis . 2002,第3期

机译：剩余格，po和BCK代数的有限可嵌入性
4. Topological Residuated Lattice: A Unifying Algebra Representation of Some Rough Set Models [C] . Xiaohong Zhang Rough sets and knowledge technology . 2009

机译：拓扑剩余格：一些粗糙集模型的统一代数表示
5. Invariant subspace problem and spectral properties of bounded linear operators on Banach spaces, Banach lattices, and topological vector spaces [D] . Troitsky, Vladimir G. 1999

机译：Banach空间，Banach格和拓扑矢量空间上有界线性算子的不变子空间问题和谱性质
6. Some New Algebraic and Topological Properties of the Minkowski Inverse in the Minkowski Space [O] . Hanifa Zekraoui, Zeyad Al-Zhour, Cenap Özel 2013

机译：Minkowski空间中Minkowski逆的一些新的代数和拓扑性质
7. Algebraic and Topological Results on Lifting Properties in Residuated Lattices [O] . Daniela Cheptea, George Georgescu 2014

机译：关于剩余格子中提升性质的代数和拓扑结果

Algebraic and topological results on lifting properties in residuated lattices

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