caa a22 4500 60547060X CHVBK 20210128100329.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s00500-014-1466-7 doi (NATIONALLICENCE)springer-10.1007/s00500-014-1466-7 The representation of square root quasi-pseudo-MV algebras [Elektronische Daten] [Wenjuan Chen, Wieslaw Dudek] $$\sqrt{'}$$ ′ 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. Springer-Verlag Berlin Heidelberg, 2014 Quasi-MV algebras nationallicence Quasi-pMV algebras nationallicence $$\sqrt{\hbox {quasi-pMV}}$$ quasi-pMV algebras nationallicence Cartesian $$\sqrt{\hbox {quasi-pMV}}$$ quasi-pMV algebras nationallicence PR-groups nationallicence Representations nationallicence Chen Wenjuan School of Mathematical Sciences, University of Jinan, No. 336, West Road of Nan Xinzhuang, 250022, Jinan, Shandong, P.R. China aut Dudek Wieslaw Institute of Mathematics and Computer Science, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370, Wrocław, Poland aut Soft Computing Springer Berlin Heidelberg 19/2(2015-02-01), 269-282 1432-7643 19:2<269 2015 19 500 https://doi.org/10.1007/s00500-014-1466-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00500-014-1466-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chen Wenjuan School of Mathematical Sciences, University of Jinan, No. 336, West Road of Nan Xinzhuang, 250022, Jinan, Shandong, P.R. China aut NATIONALLICENCE 700 1- Dudek Wieslaw Institute of Mathematics and Computer Science, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370, Wrocław, Poland aut NATIONALLICENCE 773 0- Soft Computing Springer Berlin Heidelberg 19/2(2015-02-01), 269-282 1432-7643 19:2<269 2015 19 500