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Maximal free sequences in a Boolean algebra

J. D. Monk (2011)

Commentationes Mathematicae Universitatis Carolinae

We study free sequences and related notions on Boolean algebras. A free sequence on a BA A is a sequence a ξ : ξ < α of elements of A , with α an ordinal, such that for all F , G [ α ] < ω with F < G we have ξ F a ξ · ξ G - a ξ 0 . A free sequence of length α exists iff the Stone space Ult ( A ) has a free sequence of length α in the topological sense. A free sequence is maximal iff it cannot be extended at the end to a longer free sequence. The main notions studied here are the spectrum function 𝔣 sp ( A ) = { | α | : A has an infinite maximal free sequence of length α } and the associated min-max function 𝔣 ( A ) = min ( 𝔣 sp ( A ) ) . Among the results...

Maximal MV-algebras.

Alexandru Filipoiu, George Georgescu, Ada Lettieri (1997)

Mathware and Soft Computing

In this paper we define maximal MV-algebras, a concept similar to the maximal rings and maximal distributive lattices. We prove that any maximal MV-algebra is semilocal, then we characterize a maximal MV-algebra as finite direct product of local maximal MV-algebras.

Median prime ideals of pseudo-complemented distributive lattices

M. Sambasiva Rao (2022)

Archivum Mathematicum

Coherent ideals, strongly coherent ideals, and τ -closed ideals are introduced in pseudo-complemented distributive lattices and their characterization theorems are derived. A set of equivalent conditions is derived for every ideal of a pseudo-complemented distributive lattice to become a coherent ideal. The notion of median prime ideals is introduced and some equivalent conditions are derived for every maximal ideal of a pseudo-complemented distributive lattice to become a median prime ideal which...

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