Basic pseudorings

Ivan Chajda; Miroslav Kolařík

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2009)

  • Volume: 48, Issue: 1, page 25-31
  • ISSN: 0231-9721

Abstract

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The concept of a basic pseudoring is introduced. It is shown that every orthomodular lattice can be converted into a basic pseudoring by using of the term operation called Sasaki projection. It is given a mutual relationship between basic algebras and basic pseudorings. There are characterized basic pseudorings which can be converted into othomodular lattices.

How to cite

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Chajda, Ivan, and Kolařík, Miroslav. "Basic pseudorings." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 48.1 (2009): 25-31. <http://eudml.org/doc/35186>.

@article{Chajda2009,
abstract = {The concept of a basic pseudoring is introduced. It is shown that every orthomodular lattice can be converted into a basic pseudoring by using of the term operation called Sasaki projection. It is given a mutual relationship between basic algebras and basic pseudorings. There are characterized basic pseudorings which can be converted into othomodular lattices.},
author = {Chajda, Ivan, Kolařík, Miroslav},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Basic algebra; basic pseudoring; orthomodular lattice; basic algebra; basic pseudoring; orthomodular lattice},
language = {eng},
number = {1},
pages = {25-31},
publisher = {Palacký University Olomouc},
title = {Basic pseudorings},
url = {http://eudml.org/doc/35186},
volume = {48},
year = {2009},
}

TY - JOUR
AU - Chajda, Ivan
AU - Kolařík, Miroslav
TI - Basic pseudorings
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2009
PB - Palacký University Olomouc
VL - 48
IS - 1
SP - 25
EP - 31
AB - The concept of a basic pseudoring is introduced. It is shown that every orthomodular lattice can be converted into a basic pseudoring by using of the term operation called Sasaki projection. It is given a mutual relationship between basic algebras and basic pseudorings. There are characterized basic pseudorings which can be converted into othomodular lattices.
LA - eng
KW - Basic algebra; basic pseudoring; orthomodular lattice; basic algebra; basic pseudoring; orthomodular lattice
UR - http://eudml.org/doc/35186
ER -

References

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  2. Birkhoff, G., Lattice Theory, Publ. AMS, Providence, 1967. (1967) Zbl0153.02501MR0227053
  3. Chajda, I., Halaš, R., Kühr, J., Semilattice Structures, Heldermann Verlag, Lemgo, 2007. (2007) Zbl1117.06001MR2326262
  4. Chajda, I., Kolařík, M., Independence of axiom system of basic algebras, Soft Computing 13, 1 (2009), 41–43. (2009) Zbl1178.06007
  5. Chajda, I., Länger, H., Ring-like structures corresponding to MV-algebras via symmetrical difference, Sitzungsberichte ÖAW, Math.–Naturw. Kl. Abt. II 213 (2004), 33–41. (2004) MR2251532
  6. Dorfer, G., Dvurečenskij, A., Länger H., Symmetric difference in orthomodular lattices, Math. Slovaca 46 (1996), 435–444. (1996) MR1451034
  7. Dorninger, D., Länger, H., Maczyński, M., The logic induced by a system of homomorphisms and its various algebraic characterizations, Demonstratio Math. 30 (1997), 215–232. (1997) MR1446613
  8. Dorninger, D., Länger, H., Maczyński, M., On ring-like structures occuring in axiomatic quantum mechanics, Sitzungsberichte ÖAW, Math.–Naturw. Kl. Abt. II 206 (1997), 279–289. (1997) MR1632939
  9. Dorninger, D., Länger, H., Maczyński, M., Lattice properties of ring-like quantum logics, Intern. J. of Theor. Physics 39 (2000), 1015–1026. (2000) MR1779170
  10. Shang, Y., Ring-like structures corresponding to pseudo MV-algebras, Soft Computing 13, 1 (2009), 71–76. (2009) Zbl1165.06005

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