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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.