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Abstrakty
We introduce the so-called DN-algebra whose axiomatic system is a common axiomatization of directoids with an antitone involution and the so-called D-quasiring. It generalizes the concept of Newman algebras (introduced by H. Dobbertin) for a common axiomatization of Boolean algebras and Boolean rings.
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Kategorie tematyczne
Rocznik
Tom
Numer
Strony
139-145
Opis fizyczny
Daty
wydano
2008
otrzymano
2007-05-18
poprawiono
2007-07-10
Twórcy
autor
- Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic
autor
- Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic
Bibliografia
- [1] G. Birkhoff, Lattice Theory, (3rd edition), Colloq. Publ. 25, Proc. Amer. Math. Soc., Providence, R. I., 1967.
- [2] I. Chajda and M. Kolařík, Directoids with an antitone involution, Comment. Math. Univ. Carolinae (CMUC) 48 (2007), 555-567.
- [3] I. Chajda and H. Länger, A common generalization of ortholattices and Boolean quasirings, Demonstratio Math. 15 (2007), 769-774.
- [4] H. Dobbertin, Note on associative Newman algebras, Algebra Universalis 9 (1979), 396-397.
- [5] D. Dorninger, H. Länger andM. Mączyński, The logic induced by a system of homomorphisms and its various algebraic characterizations, Demonstratio Math. 30 (1997), 215-232.
- [6] J. Ježek and R. Quackenbush, Directoids: algebraic models of up-directed sets, Algebra Universalis 27 (1990), 49-69.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1139