On a Construction of ModularGMS-algebras

Abd El-Mohsen Badawy

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2015)

  • Volume: 54, Issue: 1, page 19-31
  • ISSN: 0231-9721

Abstract

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In this paper we investigate the class of all modular GMS-algebras which contains the class of MS-algebras. We construct modular GMS-algebras from the variety 𝐊 ̲ 2 by means of K ̲ 2 -quadruples. We also characterize isomorphisms of these algebras by means of K ̲ 2 -quadruples.

How to cite

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Badawy, Abd El-Mohsen. "On a Construction of ModularGMS-algebras." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 54.1 (2015): 19-31. <http://eudml.org/doc/271643>.

@article{Badawy2015,
abstract = {In this paper we investigate the class of all modular GMS-algebras which contains the class of MS-algebras. We construct modular GMS-algebras from the variety $\mathbf \{\underline\{K\}\}_\{2\}$ by means of $\underline\{K\}_\{2\}$-quadruples. We also characterize isomorphisms of these algebras by means of $\underline\{K\}_\{2\}$-quadruples.},
author = {Badawy, Abd El-Mohsen},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {$\mathit \{MS\}$-algebras; $\mathit \{GMS\}$-algebras; $K_\{2\}$-algebras; Kleene algebras; isomorphisms},
language = {eng},
number = {1},
pages = {19-31},
publisher = {Palacký University Olomouc},
title = {On a Construction of ModularGMS-algebras},
url = {http://eudml.org/doc/271643},
volume = {54},
year = {2015},
}

TY - JOUR
AU - Badawy, Abd El-Mohsen
TI - On a Construction of ModularGMS-algebras
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2015
PB - Palacký University Olomouc
VL - 54
IS - 1
SP - 19
EP - 31
AB - In this paper we investigate the class of all modular GMS-algebras which contains the class of MS-algebras. We construct modular GMS-algebras from the variety $\mathbf {\underline{K}}_{2}$ by means of $\underline{K}_{2}$-quadruples. We also characterize isomorphisms of these algebras by means of $\underline{K}_{2}$-quadruples.
LA - eng
KW - $\mathit {MS}$-algebras; $\mathit {GMS}$-algebras; $K_{2}$-algebras; Kleene algebras; isomorphisms
UR - http://eudml.org/doc/271643
ER -

References

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  1. Badawy, A., Guffová, D., Haviar, M., Triple construction of decomposable MS-algebras, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 51, 2 (2012), 35–65. (2012) MR3058873
  2. Birkhoff, G., Lattice Theory, 3rd edition, Amer. Math. Soc. Colloq. Pub. 25, Amer. Math. Soc., Providence, R.I., 1967. (1967) Zbl0153.02501MR0227053
  3. Blyth, T. S., Varlet, J. C., On a common abstraction of De Morgan algebras and Stone algebras, Proc. Roy. Soc. Edinburgh A 94 (1983), 301–308. (1983) Zbl0536.06013MR0709723
  4. Blyth, T. S., Varlet, J. C., Sur la construction de certaines MS-algèbres, Portugaliea Math. 39 (1980), 489–496. (1980) MR0776258
  5. Blyth, T. S., Varlet, J. C., Corrigendum “Sur la construction de certaines MS-algèbres”, Portugaliea Math. 42 (1983/84), 469–471. (1983) MR0836125
  6. Chen, C. C., Grätzer, G., 10.4153/CJM-1969-096-5, Canad. J. Math. 21 (1969), 884–894. (1969) Zbl0184.03303MR0242737DOI10.4153/CJM-1969-096-5
  7. Chen, C. C., Grätzer, G., 10.4153/CJM-1969-097-2, Canad. J. Math. 21 (1969), 895–903. (1969) Zbl0184.03304MR0242738DOI10.4153/CJM-1969-097-2
  8. Haviar, M., On a certain construction of MS-algebras, Portugliae Mathematica 51 (1994), 71–83. (1994) Zbl0815.06011MR1281957
  9. Katriňák, T., 10.1002/mana.19720530109, Math. Nachrichten 53 (1972), 85–89. (1972) DOI10.1002/mana.19720530109
  10. Katriňák, T., Mederly, P., 10.1007/BF02485742, Algebra Univ. 4 (1974), 301–315. (1974) Zbl0316.06005MR0354470DOI10.1007/BF02485742
  11. Katriňák, T., Mikula, K., On a construction of MS-algebeas, Portugliae Mathematica 45 (1978), 157–163. (1978) 
  12. Ševčovič, D., Free non-distributive Morgan–Stone algebras, New Zealand J. Math. 25 (1996), 85–94. (1996) Zbl0848.06005MR1398368

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