SAI-lattices and ringoids

• Autorzy: Chajda I. , Langer H.
• Języki publikacji: EN

Abstrakty

EN

The natural bijective correspondence between Boolean algebras and Boolean rings is generalized from Boolean algebras to lattices with 0 every principal ideal of which has an antitone involution. The corresponding ring-like structures are called ring-oids. Among them orthorings are characterized by a simple axiom. It is shown that congruences on ringoids are determined by their kernels and that ringoids are permutable at 0.

Słowa kluczowe

EN

lattice; ringoid; orthoring; congruence kernel; subtractive term

PL

kraty; pierścienie; ortopierścienie; kongruencja jądra

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 3
• Strony: 483--490
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Chajda I.

autor

Langer H.

• Palacky University Olomouc Department of Algebra and Geometry Tomkova 40 77900 Olomouc, Czech Republic,

Bibliografia

• [1] G. Birkhoff, Lattice Theory, Corrected reprint of the third edition, Amer. Math. Soc., Providence, R.I., 1979.
• [2] I. Chajda, Pseudosemirings induced by ortholattices, Czechoslovak Math. J. 46 (1996), 405–411.
• [3] I. Chajda and G. Eigenthaler, A note on orthopseudorings and Boolean quasirings, Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 207 (1998), 83–94.
• [4] I. Chajda, G. Eigenthaler and H. Länger, Congruence Classes in Universal Algebra, Heldermann, Lemgo 2003.
• [5] I. Chajda and H. Länger, Ring-like operations in pseudocomplemented semilattices, Discuss. Math. General Algebra Appl. 20 (2000), 87–95.
• [6] I. Chajda and H. Länger, Orthorings, Discuss. Math. General Algebra Appl. 24 (2004), 137–147.
• [7] I. Chajda and H. Länger, Ring-like structures corresponding to MV-algebras via symmetric difference, Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 213 (2004), 33–41.
• [8] I. Chajda, H. Länger and M. Mączyński, Ring-like structures corresponding to generalized orthomodular lattices, Math. Slovaca 54 (2004), 143–150.
• [9] G. Dorfer, A. Dvurečenskij and H. Länger, Symmetric difference in orthomodular lattices, Math. Slovaca 46 (1996), 435–444.
• [10] D. Dorninger, H. Länger and M. Mączyński, The logic induced by a system of homomorphisms and its various algebraic characterizations, Demonstratio Math. 30 (1997), 215–232.
• [11] D. Dorninger, H. Länger and M. Mączyński, On ring-like structures occurring in axiomatic quantum mechanics, Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II 206 (1997), 279–289.
• [12] H. P. Gumm and A. Ursini, Ideals in universal algebras, Algebra Universalis 19 (1984), 45–54.
• [13] H. Länger, Generalizations of the correspondence between Boolean algebras and Boolean rings to orthomodular lattices, Tatra Mt. Math. Publ. 15 (1998), 97–105.