Meanders in lattices

• Autores: Ladislav Beran
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 46, Fasc. 1-2, 1995 (Ejemplar dedicado a: Professor Paul Dubreil (In memoriam )), págs. 11-20
• Idioma: inglés
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• Resumen

  • 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.