Algebraic and topological results on lifting properties in residuated lattices

作者：Georgescu George; Cheptea Daniela; Muresan Claudia^*

来源：Fuzzy Sets and Systems, 2015, 271: 102-132.

DOI：10.1016/j.fss.2014.11.007

• Universal algebra
• (Local, semilocal, maximal, hyperarchimedean, simple, semisimple) residuated lattice
• Lifting Property
• (Prime, maximal) spectrum
• Stone topology
• Reticulation

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.

• 出版日期2015-7-15