ARCHIMEDEAN RESIDUATED LATTICES

作者：Busneag Dumitru^*; Piciu Dana; Jeflea Antoneta

来源：Analele Stiintifice ale Universitatii Al I Cuza Din Iasi-Serie Noua-Matematica, 2010, 56(2): 227-252.

• residuated lattice
• boolean algebra
• archimedean
• hyperarchimedean residuated lattice
• deductive system
• irreducible element
• prime deductive system
• maximal deductive system

For a residuated lattice A we denote by Ds(A) the lattice of all deductive systems (congruence filters) of A. The aim of this paper is to put in evidence new characterizations for maximal and prime elements of Ds(A) and to characterize archimedean and hyperarchimedean residuated lattices; so we prove some theorems of Nachbin type for residuated lattices. These results generalize to the case of residuated lattices some results earlier obtained by BUSNEAG and PICIU for the case of BL-algebras.

• 出版日期2010