On product M V -algebras

Ján Jakubík

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 4, page 797-810
  • ISSN: 0011-4642

Abstract

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In this paper we apply the notion of the product M V -algebra in accordance with the definition given by B. Riečan. We investigate the convex embeddability of an M V -algebra into a product M V -algebra. We found sufficient conditions under which any two direct product decompositions of a product M V -algebra have isomorphic refinements.

How to cite

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Jakubík, Ján. "On product $MV$-algebras." Czechoslovak Mathematical Journal 52.4 (2002): 797-810. <http://eudml.org/doc/30745>.

@article{Jakubík2002,
abstract = {In this paper we apply the notion of the product $MV$-algebra in accordance with the definition given by B. Riečan. We investigate the convex embeddability of an $MV$-algebra into a product $MV$-algebra. We found sufficient conditions under which any two direct product decompositions of a product $MV$-algebra have isomorphic refinements.},
author = {Jakubík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {$MV$-algebras; product; convex; embedding; direct; decomposition; MV-algebra; product MV-algebra; convex embedding; direct product decomposition},
language = {eng},
number = {4},
pages = {797-810},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On product $MV$-algebras},
url = {http://eudml.org/doc/30745},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Jakubík, Ján
TI - On product $MV$-algebras
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 4
SP - 797
EP - 810
AB - In this paper we apply the notion of the product $MV$-algebra in accordance with the definition given by B. Riečan. We investigate the convex embeddability of an $MV$-algebra into a product $MV$-algebra. We found sufficient conditions under which any two direct product decompositions of a product $MV$-algebra have isomorphic refinements.
LA - eng
KW - $MV$-algebras; product; convex; embedding; direct; decomposition; MV-algebra; product MV-algebra; convex embedding; direct product decomposition
UR - http://eudml.org/doc/30745
ER -

References

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  1. Independent axiomatization for M V -algebras, Tatra Mt. Math. Publ. 15 (1998), 227–232. (1998) MR1655091
  2. Algebraic Foundations of Many-Valued Reasoning, Kluwer Academic Publishers, Dordrecht, 2000. (2000) MR1786097
  3. Lattice Ordered Groups, Tulane University, 1971. (1971) Zbl0235.06006
  4. Product M V -algebras, Multiple Valued Logic 6 (2001), 193–251. (2001) MR1777248
  5. 10.1006/jmaa.1999.6353, J.  Math. Anal. Appl. 234 (1999), 208–222. (1999) MR1694841DOI10.1006/jmaa.1999.6353
  6. Partially Ordered Algebraic Systems, Pergamon Press, Oxford, 1964. (1964) MR0218283
  7. Cyclic ordered groups and M V -algebras, Czechoslovak Math.  J. 43(118) (1993), 249–263. (1993) Zbl0795.06015MR1211747
  8. Direct product decompositions of M V -algebras, Czechoslovak Math.  J. 44(119) (1994), 725–739. (1994) MR1295146
  9. On complete M V -algebras, Czechoslovak Math.  J. 45(120) (1995), 473–480. (1995) MR1344513
  10. 10.1016/0022-1236(86)90015-7, J.  Funct. Anal. 65 (1986), 15–63. (1986) DOI10.1016/0022-1236(86)90015-7
  11. On the product M V -algebras, Tatra Mt. Math. Publ. 16 (1999), 143–149. (1999) MR1725292

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