A common approach to directoids with an antitone involution and D-quasirings

• Autorzy: Ivan Chajda , Miroslav Kolařík
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

directoid; antitone involution; D-quasiring; DN-algebra; a-mutation

Kategorie tematyczne

• 06E20: Ring-theoretic properties
• 06A12: Semilattices
• 06A06: Partial order, general

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2008
• Tom: 28
• Numer: 2
• Strony: 139-145

Daty

wydano

2008

otrzymano

2007-05-18

poprawiono

2007-07-10

Twórcy

autor

Ivan Chajda

• Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic

autor

Miroslav Kolařík

• 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.

Identyfikatory

DOI

10.7151/dmgaa.1139