Facebook Instagram Twitter RSS Feed PodBean Back to top on side

An example of a commutative basic algebra which is not an MV-algebra

In: Mathematica Slovaca, vol. 60, no. 2
Michal Botur
Detaily:
Rok, strany: 2010, 171 - 178
Kľúčové slová:
basic algebra, lattice with sectional antitone involutions, MV-algebra
O článku:
Many algebras arising in logic have a lattice structure with intervals being equipped with antitone involutions. It has been proved in [CHK1] that these lattices are in a one-to-one correspondence with so-called basic algebras. In the recent papers [BOTUR, M.—HALAŠ, R.: \textit{Finite commutative basic algebras are MV-algebras}, J. Mult.-Valued Logic Soft Comput. (To appear)]. and [BOTUR, M.—HALAŠ, R.: \textit{Complete commutative basic algebras}, Order \textbf{24} (2007), 89–105] we have proved that every finite commutative basic algebra is an MV-algebra, and that every complete commutative basic algebra is a subdirect product of chains. The paper solves in negative the open question posed in [BOTUR, M.—HALAŠ, R.: \textit{Complete commutative basic algebras}, Order \textbf{24} (2007), 89–105] whether every commutative basic algebra on the interval $[0,1]$ of the reals has to be an MV-algebra.
Ako citovať:
ISO 690:
Botur, M. 2010. An example of a commutative basic algebra which is not an MV-algebra. In Mathematica Slovaca, vol. 60, no.2, pp. 171-178. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0003-0

APA:
Botur, M. (2010). An example of a commutative basic algebra which is not an MV-algebra. Mathematica Slovaca, 60(2), 171-178. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0003-0
O vydaní: