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

Discussiones Mathematicae - General Algebra and Applications (2008)

- Volume: 28, Issue: 2, page 139-145
- ISSN: 1509-9415

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topIvan Chajda, and Miroslav Kolařík. "A common approach to directoids with an antitone involution and D-quasirings." Discussiones Mathematicae - General Algebra and Applications 28.2 (2008): 139-145. <http://eudml.org/doc/276856>.

@article{IvanChajda2008,

abstract = {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.},

author = {Ivan Chajda, Miroslav Kolařík},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {directoid; antitone involution; D-quasiring; DN-algebra; a-mutation; -quasiring; -algebra; -mutation; Newman algebra},

language = {eng},

number = {2},

pages = {139-145},

title = {A common approach to directoids with an antitone involution and D-quasirings},

url = {http://eudml.org/doc/276856},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Ivan Chajda

AU - Miroslav Kolařík

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

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2008

VL - 28

IS - 2

SP - 139

EP - 145

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/276856

ER -

## References

top- [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. Zbl1199.06012
- [3] I. Chajda and H. Länger, A common generalization of ortholattices and Boolean quasirings, Demonstratio Math. 15 (2007), 769-774. Zbl1160.08003
- [4] H. Dobbertin, Note on associative Newman algebras, Algebra Universalis 9 (1979), 396-397. Zbl0445.06010
- [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. Zbl0879.06005
- [6] J. Ježek and R. Quackenbush, Directoids: algebraic models of up-directed sets, Algebra Universalis 27 (1990), 49-69. Zbl0699.08002

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