Geodesic
Ring-like structures derived from $\lambda $-lattices with antitone involutions
Mathematica Bohemica, Tome 132 (2007) no. 1, pp. 87-96

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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.
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.
DOI : 10.21136/MB.2007.133992
Classification : 06A12, 06B99, 06C15, 16Y99, 81P10
Keywords: $\lambda $-lattice; $\lambda $-semilattice; ortholattice; $\lambda $-ortholattice; antitone involution; Boolean quasiring 
Chajda, Ivan. Ring-like structures derived from $\lambda $-lattices with antitone involutions. Mathematica Bohemica, Tome 132 (2007) no. 1, pp. 87-96. doi: 10.21136/MB.2007.133992
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[1] G. Birkhof: Lattice Theory. (Third edition.) Amer. Math. Soc. Colloq. Publ. 25, Providence, RI, 1979. | MR

[2] L. Beran: Orthomodular Lattices. Reidel Publ., Dordrecht, 1985. | MR | Zbl

[3] I. Chajda: Pseudorings induced by ortholattices. Czechoslovak Math. J. 46 (1996), 405–411. | MR

[4] I. Chajda, G. Eigenthaler: A note on orthopseudorings and Boolean quasirings. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 207 (1998), 83–94. | MR

[5] I. Chajda, H. Länger, M. Mączyński: Ring-like structures corresponding to generalized orthomodular lattices. Math. Slovaca 54 (2004), 143–150. | MR

[6] D. Dorminger, H. Länger, M. Mączyński: The logic induced by a system of homomorphisms and its algebraic characterizations. Demonstratio Math. 30 (1997), 215–232.

[7] D. Dorminger, H. Länger, M. Mączyński: On ring-like structures occuring in axiomatic quantum mechanics. Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 206 (1997), 279–289.

[8] G. Grätzer: General Lattice Theory. Birkhäuser, Basel, 1978. | MR

[9] J. Ježek, R. Quackenbush: Directoids: algebraic models of up-directed sets. Algebra Univers. 27 (1990), 49–69. | DOI | MR

[10] G. Kalmbach: Orthomodular Lattices. Academic Press, London, 1983. | MR | Zbl

[11] J. Karásek: Rotations of $\lambda $-lattices. Math. Bohem. 121 (1996), 293–300. | MR

[12] H. Länger: Generalizations of the correspondence between Boolean algebras and Boolean rings to orthomodular lattices. Tatra Mt. Math. Publ. 15 (1998), 97–105. | MR

[13] V. Snášel: $\lambda $-Lattices. Math. Bohem. 122 (1997), 267–272. | MR

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