There exist subdirectly irreducible commutative basic algebras of an arbitrary infinite cardinality which are not MV-algebras

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F11%3A33116595" target="_blank" >RIV/61989592:15310/11:33116595 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1007/s00012-011-0123-6" target="_blank" >http://dx.doi.org/10.1007/s00012-011-0123-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00012-011-0123-6" target="_blank" >10.1007/s00012-011-0123-6</a>

Result language

angličtina

Original language name

There exist subdirectly irreducible commutative basic algebras of an arbitrary infinite cardinality which are not MV-algebras

Original language description

It was recently proved by P. Wojciechowski that for any infinite cardinal there exists a linearly ordered MV-algebra of this cardinality. Since basic algebras are a (non-associative) generalization of MV-algebras, there rises a natural question if this is true also for basic algebras which are not MV-algebras. Using the construction by P. Wojciechowski and the modified construction by the first author, we can set up certain defectors which enable us to prove the result of the title.

Czech name

—

Czech description

—

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

—

Project

—

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2011

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Algebra Universalis

ISSN

0002-5240

e-ISSN

—

Volume of the periodical

65

Issue of the periodical within the volume

2

Country of publishing house

CH - SWITZERLAND

Number of pages

8

Pages from-to

185-192

UT code for WoS article

000288954600004

EID of the result in the Scopus database

—