Resumen de Meanders in lattices

Ladislav Beran

• Let $I$ be an ideal of a lattice $L$ where $0, 1\in L$. Let $I^0 := I$ and let the $n$-th meander $I^n$ of $I$ be defined recursively by $I^n = \{w\in L; \forall t\in L$ $w\oplus t\in I^{n-1}\Rightarrow t\in I^{n-1}\}$ where $w\oplus t$ denotes $w\wedge t$ for $n$ odd and $w\oplus t = w\vee t$ for $n$ even. Dually is defined the $n$-th meander $F^n$ of a filter $F$. In this paper we study the meanders of semiprime and prime ideals and we establish some basic properties of meanders.