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

Ivan Chajda; Miroslav Kolařík

Discussiones Mathematicae - General Algebra and Applications (2008)

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

Abstract

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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.

How to cite

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Ivan 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

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  1. [1] G. Birkhoff, Lattice Theory, (3rd edition), Colloq. Publ. 25, Proc. Amer. Math. Soc., Providence, R. I., 1967. 
  2. [2] I. Chajda and M. Kolařík, Directoids with an antitone involution, Comment. Math. Univ. Carolinae (CMUC) 48 (2007), 555-567. Zbl1199.06012
  3. [3] I. Chajda and H. Länger, A common generalization of ortholattices and Boolean quasirings, Demonstratio Math. 15 (2007), 769-774. Zbl1160.08003
  4. [4] H. Dobbertin, Note on associative Newman algebras, Algebra Universalis 9 (1979), 396-397. Zbl0445.06010
  5. [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. [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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