The representation of square root quasi-pseudo-MV algebras
| LEADER | caa a22 4500 | ||
|---|---|---|---|
| 001 | 60547060X | ||
| 003 | CHVBK | ||
| 005 | 20210128100329.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20150201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00500-014-1466-7 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00500-014-1466-7 | ||
| 245 | 0 | 4 | |a The representation of square root quasi-pseudo-MV algebras |h [Elektronische Daten] |c [Wenjuan Chen, Wieslaw Dudek] |
| 520 | 3 | |a $$\sqrt{'}$$ ′ quasi-MV algebras arising from quantum computation are term expansions of quasi-MV algebras. In this paper, we introduce a generalization of $$\sqrt{'}$$ ′ quasi-MV algebras, called square root quasi-pseudo-MV algebras ( $$\sqrt{\hbox {quasi-pMV}}$$ quasi-pMV algebras, for short). First, we investigate the related properties of $$\sqrt{\hbox {quasi-pMV}}$$ quasi-pMV algebras and characterize two special types: Cartesian and flat $$\sqrt{\hbox {quasi-pMV}}$$ quasi-pMV algebras. Second, we present two representations of $$\sqrt{\hbox {quasi-pMV}}$$ quasi-pMV algebras. Furthermore, we generalize the concepts of PR-groups to non-commutative case and prove that the interval of a non-commutative PR-group with strong order unit is a Cartesian $$\sqrt{\hbox {quasi-pMV}}$$ quasi-pMV algebra. Finally, we introduce non-commutative PR-groupoids which extend abelian PR-groupoids and show that the category of negation groupoids with operators and the category of non-commutative PR-groupoids are equivalent. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Quasi-MV algebras |2 nationallicence | |
| 690 | 7 | |a Quasi-pMV algebras |2 nationallicence | |
| 690 | 7 | |a $$\sqrt{\hbox {quasi-pMV}}$$ quasi-pMV algebras |2 nationallicence | |
| 690 | 7 | |a Cartesian $$\sqrt{\hbox {quasi-pMV}}$$ quasi-pMV algebras |2 nationallicence | |
| 690 | 7 | |a PR-groups |2 nationallicence | |
| 690 | 7 | |a Representations |2 nationallicence | |
| 700 | 1 | |a Chen |D Wenjuan |u School of Mathematical Sciences, University of Jinan, No. 336, West Road of Nan Xinzhuang, 250022, Jinan, Shandong, P.R. China |4 aut | |
| 700 | 1 | |a Dudek |D Wieslaw |u Institute of Mathematics and Computer Science, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370, Wrocław, Poland |4 aut | |
| 773 | 0 | |t Soft Computing |d Springer Berlin Heidelberg |g 19/2(2015-02-01), 269-282 |x 1432-7643 |q 19:2<269 |1 2015 |2 19 |o 500 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00500-014-1466-7 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00500-014-1466-7 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Chen |D Wenjuan |u School of Mathematical Sciences, University of Jinan, No. 336, West Road of Nan Xinzhuang, 250022, Jinan, Shandong, P.R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Dudek |D Wieslaw |u Institute of Mathematics and Computer Science, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370, Wrocław, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Soft Computing |d Springer Berlin Heidelberg |g 19/2(2015-02-01), 269-282 |x 1432-7643 |q 19:2<269 |1 2015 |2 19 |o 500 | ||