A complete invariant system for noetherian BL-algebras and more general L-algebras

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2025-03-07 DOI:10.1016/j.apal.2025.103580

Wolfgang Rump

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引用次数: 0

Abstract

Main results on BL-algebras, including their classification in the finite case, are reconsidered and extended to a class of L-algebras X with prime factorization, including BL-algebras with ascending chain condition for its lattice. The weighted forest associated with a finite BL-algebra reappears as a canonical L-subalgebra

\tilde{P} (X)

of prime elements in the self-similar closure

S (X)

where

\tilde{P} (X)

is completely determined by its underlying poset (not necessarily a forest), while the weights are associated with existing powers of the prime elements in X. These invariants determine X within its self-similar closure

S (X) = S (\tilde{P} (X))

. The three basic types of BL-algebras are related to concepts of L-algebras with further-reaching significance in quantum theory.

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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.