# Higher degrees of distributivity in $MV$-algebras

Czechoslovak Mathematical Journal (2003)

- Volume: 53, Issue: 3, page 641-653
- ISSN: 0011-4642

## Access Full Article

top## Abstract

top## How to cite

topJakubík, Ján. "Higher degrees of distributivity in $MV$-algebras." Czechoslovak Mathematical Journal 53.3 (2003): 641-653. <http://eudml.org/doc/30806>.

@article{Jakubík2003,

abstract = {In this paper we deal with the of an $MV$-algebra $\mathcal \{A\}$, where $\alpha $ and $\beta $ are nonzero cardinals. It is proved that if $\mathcal \{A\}$ is singular and $(\alpha ,2)$-distributive, then it is . We show that if $\mathcal \{A\}$ is complete then it can be represented as a direct product of $MV$-algebras which are homogeneous with respect to higher degrees of distributivity.},

author = {Jakubík, Ján},

journal = {Czechoslovak Mathematical Journal},

keywords = {$MV$-algebra; archimedean $MV$-algebra; completeness; singular $MV$-algebra; higher degrees of distributivity; MV-algebra; archimedean MV-algebra; completeness; singular MV-algebra; higher degrees of distributivity},

language = {eng},

number = {3},

pages = {641-653},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Higher degrees of distributivity in $MV$-algebras},

url = {http://eudml.org/doc/30806},

volume = {53},

year = {2003},

}

TY - JOUR

AU - Jakubík, Ján

TI - Higher degrees of distributivity in $MV$-algebras

JO - Czechoslovak Mathematical Journal

PY - 2003

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 53

IS - 3

SP - 641

EP - 653

AB - In this paper we deal with the of an $MV$-algebra $\mathcal {A}$, where $\alpha $ and $\beta $ are nonzero cardinals. It is proved that if $\mathcal {A}$ is singular and $(\alpha ,2)$-distributive, then it is . We show that if $\mathcal {A}$ is complete then it can be represented as a direct product of $MV$-algebras which are homogeneous with respect to higher degrees of distributivity.

LA - eng

KW - $MV$-algebra; archimedean $MV$-algebra; completeness; singular $MV$-algebra; higher degrees of distributivity; MV-algebra; archimedean MV-algebra; completeness; singular MV-algebra; higher degrees of distributivity

UR - http://eudml.org/doc/30806

ER -

## References

top- 10.1007/BF01136029, Math. Z. 101 (1967), 123–130. (1967) MR0218284DOI10.1007/BF01136029
- Algebraic Foundations of Many-valued Reasoning. Trends in Logic, Studia Logica Library, Vol. 7, Kluwer Academic Publishers, Dordrecht, 2000. (2000) MR1786097
- 10.2140/pjm.1964.14.493, Pacific J. Math. 14 (1964), 494–499. (1964) Zbl0122.03701MR0166279DOI10.2140/pjm.1964.14.493
- Lattice Ordered Groups, Tulane University, 1970. (1970) Zbl0258.06011
- Partially Ordered Algebraic Systems, Pergamon Press, Oxford, 1963. (1963) Zbl0137.02001MR0171864
- Higher degrees of distributivity in lattices and lattice ordered groups, Czechoslovak Math. J. 18 (1968), 356–376. (1968) MR0225690
- Distributivity in lattice ordered groups, Czechoslovak Math. J. 22 (1972), 108–125. (1972) MR0325487
- Direct product decompositions of $MV$-algebras, Czechoslovak Math. J. 44 (1994), 725–739. (1994)
- On complete $MV$-algebras, Czechoslovak Math. J. 45 (1995), 473–480. (1995) MR1344513
- 10.1023/A:1022436113418, Czechoslovak Math. J. 48 (1998), 575–582. (1998) MR1637871DOI10.1023/A:1022436113418
- 10.1023/A:1022440214327, Czechoslovak Math. J. 48 (1998), 597–608. (1998) MR1637863DOI10.1023/A:1022440214327
- 10.1307/mmj/1028999839, Michigan Math. J. 14 (1967), 393–400. (1967) Zbl0167.30202MR0219462DOI10.1307/mmj/1028999839
- 10.2140/pjm.1957.7.983, Pacific J. Math. 7 (1957), 983–992. (1957) Zbl0086.02803MR0089180DOI10.2140/pjm.1957.7.983
- Boolean Algebras, Second Edition, Springer Verlag, Berlin, 1964. (1964) MR0126393
- Über subdirekte Summen geordneter Gruppen, Czechoslovak Math. J. 10 (1960), 400–424. (1960) MR0123626
- 10.1090/S0002-9947-1962-0138569-8, Trans. Amer. Math. Soc. 104 (1962), 334–346. (1962) Zbl0105.09401MR0138569DOI10.1090/S0002-9947-1962-0138569-8
- 10.2140/pjm.1962.12.1131, Pacific J. Math. 12 (1962), 1131–1148. (1962) Zbl0111.24301MR0147549DOI10.2140/pjm.1962.12.1131

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.