Completions of GBL-algebras: Negative results

Tomasz Kowalski; Tadeusz Litak

doi:10.1007/s00012-008-2056-2

Completions of GBL-algebras: Negative results

Tomasz Kowalski^*
, Tadeusz Litak

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

We provide a simple sufficient criterion to show that a given variety of GBL-algebras does not admit (local) completions. As corollaries, we obtain that no variety of GBL-algebras containing Chang's chain, no nontrivial variety of ℓ-groups, nor the variety of product algebras admit completions. The first result strengthens a result of Gehrke and Priestley.

Original language	English
Pages (from-to)	373-384
Number of pages	12
Journal	Algebra Universalis
Volume	58
Issue number	4
DOIs	https://doi.org/10.1007/s00012-008-2056-2
Publication status	Published - Aug 2008

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title = "Completions of GBL-algebras: Negative results",

abstract = "We provide a simple sufficient criterion to show that a given variety of GBL-algebras does not admit (local) completions. As corollaries, we obtain that no variety of GBL-algebras containing Chang's chain, no nontrivial variety of ℓ-groups, nor the variety of product algebras admit completions. The first result strengthens a result of Gehrke and Priestley.",

keywords = "BL-algebras, Canonicity, Completions, MV-algebras, ℓ-groups",

author = "Tomasz Kowalski and Tadeusz Litak",

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T2 - Negative results

AU - Kowalski, Tomasz

AU - Litak, Tadeusz

PY - 2008/8

Y1 - 2008/8

N2 - We provide a simple sufficient criterion to show that a given variety of GBL-algebras does not admit (local) completions. As corollaries, we obtain that no variety of GBL-algebras containing Chang's chain, no nontrivial variety of ℓ-groups, nor the variety of product algebras admit completions. The first result strengthens a result of Gehrke and Priestley.

AB - We provide a simple sufficient criterion to show that a given variety of GBL-algebras does not admit (local) completions. As corollaries, we obtain that no variety of GBL-algebras containing Chang's chain, no nontrivial variety of ℓ-groups, nor the variety of product algebras admit completions. The first result strengthens a result of Gehrke and Priestley.

KW - BL-algebras

KW - Canonicity

KW - Completions

KW - MV-algebras

KW - ℓ-groups

UR - https://www.scopus.com/pages/publications/52049090579

U2 - 10.1007/s00012-008-2056-2

DO - 10.1007/s00012-008-2056-2

M3 - Article

SN - 0002-5240

VL - 58

SP - 373

EP - 384

JO - Algebra Universalis

JF - Algebra Universalis

IS - 4

ER -

Completions of GBL-algebras: Negative results

Abstract

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