We consider general functional medial and paramedial equations with four object variables. We give analogous of khown results with quasigroup operations for a class of strong dependable operations. As a consequence of these results, an analogous linear representation for every operation of a binary algebra satisfying one of these hyperidentities is obtained. Nevertheless, co-medial and co-paramedial algebras may have nonlinear binary operations.
Download file
Counter downloads: 7
- Title Medial and paramedial general identities for strong dependance operations
- Headline Medial and paramedial general identities for strong dependance operations
- Publesher
Tomsk State University - Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 65
- Date:
- DOI 10.17223/20710410/65/2
Keywords
n-ary quasigroup, strong dependent operation, medial and paramedial operations, linear representationAuthors
References
Черемушкин А. В. Аналоги теорем Глускина - Хоссу и Малышева для случая сильно зависимых n-арных операций // Дискретная математика. 2018. Т. 30. №2. С. 138-147.
Черемушкин А. В. Теорема Поста для сильно зависимых n-арных полугрупп // Дискретная математика. 2019. Т.31. У 2. С. 152-157.
Черемушкин А. В. Частично обратимые сильно зависимые n-арные операции // Матем. сб. 2020. Т. 211. №2. С. 141-158.
Toyoda К. On axioms of linear functions // Proc. Imp. Acad. Tokyo. 1941. V. 17. P. 221-227.
Němec P. and Kepka T. T-quasigroups (Part I) // Acta Univ. Carolinae. Math. Phis. 1971. V. 1. P. 39 49.
Ehsani A. Representation of the medial-like algebras // TACL 2013. N. Galatos, A. Kurz, and C. Tsinakis (eds.). ЕРІС Ser. 2013. V.25. P.64-67.
Cho J. R., Ježek J., and Керка T. Paramedial groupoids // Czechoslovak Math. J. 1999. V. 49. No. 2. P. 277-290.
Ehsani A., Movsisyan Y., and Arslanov M. A representation of paramedial n-ary groupoids // Asian-Europ. J. Math. 2014. V. 7. No. 1. P. 1450020-1-1450020-17.
Черемушкин А. В. Медиальные сильно зависимые n-арные операции // Дискретная математика. 2020. Т.32. №2. С. 112-121.
Черемушкин А. В. Парамедиальные сильно зависимые n-арные операции // Дискретная математика. 2024. Т.26. № 3. С. 115-126.
J. Aczél, V. Belousov, M. Hosszú Generalized associativity and bisymmetrv on quasigroups // Acta Math. Acad. Sci. Hungar. 1960. V. 11. No. 11-2. P. 127-136.
Nazari E. and Movsisyan Y.M. Transitive modes // Demonstratio Math. 2011. V. 44. No. 3. P.511-522.
Ehsani A. Linear representation of algebras with non-associative operations which are satisfy in the balanced functional equations //j. Phvs. Conf. Ser. 2015. V. 622. Article 012037.
Ehsani A., Krapež A., and Movsisyan Y. Algebras with parastrophicallv uncancellable quasigroup equations // Buletinul Academiei de Stiinte a Republicii Moldova. Matematica. 2016. No. 1. P.41-63.
Черемушкин А. В. Бесповторная декомпозиция сильно зависимых функций // Дискретная математика. 2004. Т. 16. № 3. С.3-42.
Sokhatsky F. and Kirka D. Canonical decompositions of solutions of functional equation of generalized medialitv // XII Intern. Algebraic Conf. Ukraine, 2019. P. 107-108.
Ehsani A. On medial-like functional equations // Math. Problems of Computer Sci. 2021. V. 38. P. 53-55.
Ehsani A. and Movsisyan Y. Linear representation of medial-like algebras // Comm. Algebra. 2013. V. 41. No. 9. P.3429-3444.
Ehsani A., Krapez A., and Movsisyan Y. Algebras with Medial-Like Functional Equations on Quasigroups, https://arxiv.org/abs/1505.06224. 2015.
Murdoch D. С. Quasi-groups which satisfy certain generalized associative laws // Amer. J. Math. 1939. V.61.2. P.509-522.
Etherington I. M. H. Groupoids with additive endomorphisms // Amer. Math. Monthly. 1958. V. 65(8P1). P.596-601.
Gligoroski D. Entropoid Based Cryptography. IACR Cryptology ePrint Archive 2021/469. https://eprint.iacr.org/2021/469. 2021.
Medial and paramedial general identities for strong dependance operations | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2024. № 65. DOI: 10.17223/20710410/65/2
Download full-text version
Counter downloads: 69