A note on medial division groupoids
HTML articles powered by AMS MathViewer
- by J. Ježek and T. Kepka PDF
- Proc. Amer. Math. Soc. 119 (1993), 423-426 Request permission
Abstract:
In 1949 Sholander showed that every medial cancellation groupoid can be embedded into a medial quasigroup. In this note we prove the dual assertion that every medial division groupoid is a homomorphic image of a medial quasigroup.References
- I. P. Cornfeld, S. V. Fomin, and Ya. G. Sinaĭ, Ergodic theory, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 245, Springer-Verlag, New York, 1982. Translated from the Russian by A. B. Sosinskiĭ. MR 832433, DOI 10.1007/978-1-4615-6927-5
- Jaroslav Ježek and Tomáš Kepka, Medial groupoids, Rozpravy Československé Akad. Věd Řada Mat. Přírod. Věd 93 (1983), no. 2, 93 (English, with Russian summary). MR 734873
- A. B. Romanowska and J. D. H. Smith, Modal theory: an algebraic approach to order, geometry, and convexity, Research and Exposition in Mathematics, vol. 9, Heldermann Verlag, Berlin, 1985. MR 788695
- Marlow Sholander, On the existence of the inverse operation in alternation groupoids, Bull. Amer. Math. Soc. 55 (1949), 746–757. MR 31493, DOI 10.1090/S0002-9904-1949-09275-3
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 423-426
- MSC: Primary 20N02
- DOI: https://doi.org/10.1090/S0002-9939-1993-1151812-7
- MathSciNet review: 1151812