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

top
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

top

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

top
  1. Lattice Theory, (Third edition.) Amer. Math. Soc. Colloq. Publ. 25, Providence, RI, 1979. (1979) MR0598630
  2. Orthomodular Lattices, Reidel Publ., Dordrecht, 1985. (1985) Zbl0583.06008MR0784029
  3. Pseudorings induced by ortholattices, Czechoslovak Math. J. 46 (1996), 405–411. (1996) MR1408295
  4. A note on orthopseudorings and Boolean quasirings, Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 207 (1998), 83–94. (1998) MR1749914
  5. Ring-like structures corresponding to generalized orthomodular lattices, Math. Slovaca 54 (2004), 143–150. (2004) MR2074211
  6. The logic induced by a system of homomorphisms and its algebraic characterizations, Demonstratio Math. 30 (1997), 215–232. (1997) 
  7. On ring-like structures occuring in axiomatic quantum mechanics, Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 206 (1997), 279–289. (1997) 
  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

NotesEmbed ?

top

You must be logged in to post comments.