Ring-like structures derived from λ -lattices with antitone involutions

Ivan Chajda

Mathematica Bohemica (2007)

  • Volume: 132, Issue: 1, page 87-96
  • ISSN: 0862-7959

Abstract

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Using the concept of the λ -lattice introduced recently by V. Snášel we define λ -lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.

How to cite

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Chajda, Ivan. "Ring-like structures derived from $\lambda $-lattices with antitone involutions." Mathematica Bohemica 132.1 (2007): 87-96. <http://eudml.org/doc/250249>.

@article{Chajda2007,
abstract = {Using the concept of the $\lambda $-lattice introduced recently by V. Snášel we define $\lambda $-lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.},
author = {Chajda, Ivan},
journal = {Mathematica Bohemica},
keywords = {$\lambda $-lattice; $\lambda $-semilattice; ortholattice; $\lambda $-ortholattice; antitone involution; Boolean quasiring; -semilattice; -ortholattice},
language = {eng},
number = {1},
pages = {87-96},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Ring-like structures derived from $\lambda $-lattices with antitone involutions},
url = {http://eudml.org/doc/250249},
volume = {132},
year = {2007},
}

TY - JOUR
AU - Chajda, Ivan
TI - Ring-like structures derived from $\lambda $-lattices with antitone involutions
JO - Mathematica Bohemica
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 132
IS - 1
SP - 87
EP - 96
AB - Using the concept of the $\lambda $-lattice introduced recently by V. Snášel we define $\lambda $-lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.
LA - eng
KW - $\lambda $-lattice; $\lambda $-semilattice; ortholattice; $\lambda $-ortholattice; antitone involution; Boolean quasiring; -semilattice; -ortholattice
UR - http://eudml.org/doc/250249
ER -

References

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  8. General Lattice Theory, Birkhäuser, Basel, 1978. (1978) MR0504338
  9. 10.1007/BF01190253, Algebra Univers. 27 (1990), 49–69. (1990) MR1025835DOI10.1007/BF01190253
  10. Orthomodular Lattices, Academic Press, London, 1983. (1983) Zbl0528.06012MR0716496
  11. Rotations of λ -lattices, Math. Bohem. 121 (1996), 293–300. (1996) MR1419883
  12. Generalizations of the correspondence between Boolean algebras and Boolean rings to orthomodular lattices, Tatra Mt. Math. Publ. 15 (1998), 97–105. (1998) MR1655082
  13. λ -Lattices, Math. Bohem. 122 (1997), 267–272. (1997) MR1600648

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