Claudia Muresan: Dense Elements and Classes of Residuated Lattices, p.11-24

Abstract:

In this paper we study the dense elements and the radical of a residuated lattice, residuated lattices with lifting Boolean center, simple, local, semilocal and quasi-local residuated lattices. BL-algebras have lifting Boolean center; moreover, Glivenko residuated lattices which fulfill the equation $(\neg \, a\rightarrow \neg \, b)\rightarrow \neg \, b=(\neg \, b\rightarrow \neg \, a)\rightarrow \neg \, a$ have lifting Boolean center.

Key Words: Residuated lattices, maximal filters, dense elements, lifting Boolean center.

2000 Mathematics Subject Classification: Primary: 06F35,
Secondary: 03G10.

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