On some types of radical classes

Ján Jakubík

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 3, page 833-848
  • ISSN: 0011-4642

Abstract

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Let 𝔪 be an infinite cardinal. We denote by C 𝔪 the collection of all 𝔪 -representable Boolean algebras. Further, let C 𝔪 0 be the collection of all generalized Boolean algebras B such that for each b ∈ B , the interval [ 0 , b ] of B belongs to C 𝔪 . In this paper we prove that C 𝔪 0 is a radical class of generalized Boolean algebras. Further, we investigate some related questions concerning lattice ordered groups and generalized M V -algebras.

How to cite

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Jakubík, Ján. "On some types of radical classes." Czechoslovak Mathematical Journal 58.3 (2008): 833-848. <http://eudml.org/doc/37871>.

@article{Jakubík2008,
abstract = {Let $\mathfrak \{m\}$ be an infinite cardinal. We denote by $C_\mathfrak \{m\}$ the collection of all $\mathfrak \{m\}$-representable Boolean algebras. Further, let $C_\mathfrak \{m\}^0$ be the collection of all generalized Boolean algebras $B$ such that for each $b\in B$, the interval $[0,b]$ of $B$ belongs to $C_\mathfrak \{m\}$. In this paper we prove that $C_\mathfrak \{m\}^0$ is a radical class of generalized Boolean algebras. Further, we investigate some related questions concerning lattice ordered groups and generalized $MV$-algebras.},
author = {Jakubík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {Boolean algebra; generalized Boolean algebra; $\mathfrak \{m\}$-representability; lattice ordered group; generalized $MV$-algebra; radical class; Boolean algebra; generalized Boolean algebra; -representability; lattice-ordered group},
language = {eng},
number = {3},
pages = {833-848},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On some types of radical classes},
url = {http://eudml.org/doc/37871},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Jakubík, Ján
TI - On some types of radical classes
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 3
SP - 833
EP - 848
AB - Let $\mathfrak {m}$ be an infinite cardinal. We denote by $C_\mathfrak {m}$ the collection of all $\mathfrak {m}$-representable Boolean algebras. Further, let $C_\mathfrak {m}^0$ be the collection of all generalized Boolean algebras $B$ such that for each $b\in B$, the interval $[0,b]$ of $B$ belongs to $C_\mathfrak {m}$. In this paper we prove that $C_\mathfrak {m}^0$ is a radical class of generalized Boolean algebras. Further, we investigate some related questions concerning lattice ordered groups and generalized $MV$-algebras.
LA - eng
KW - Boolean algebra; generalized Boolean algebra; $\mathfrak {m}$-representability; lattice ordered group; generalized $MV$-algebra; radical class; Boolean algebra; generalized Boolean algebra; -representability; lattice-ordered group
UR - http://eudml.org/doc/37871
ER -

References

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