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Automated theorem proving in quasigroup and loop theory [PDF]

AI Communications, 2010
We survey all known results in the area of quasigroup and loop theory to have been obtained with the assistance of automated theorem provers. We provide both informal and formal descriptions of selected problems, and compare the performance of selected state-of-the art first order theorem provers on them.
Phillips, J D, Stanovsky, D
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Smooth Quasigroups and Loops

1999
This monograph written by a leading specialist in this new rapidly developing field of mathematics presents the complete up-to-date theory of smooth quasigroups and loops, as well as its geometric and algebraic applications. Based on a generalization of the Lie group theory, it establishes a new background for differential geometry in the form of the ...
Sabinin Lev V., Goldberg Vladislav
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Some Varieties of Quasigroups, Loops and their Parastrophes

Communications in Mathematics and Applications, 2012
El papel de las parásitas en la teoría de los cuasigrupos y los bucles es bien conocido. Es nuestro enfoque investigar clases notables de bucles y cuasigrupos y relacionarlos con sus parásitos. Se presentan algunas consecuencias para los bucles de código.
Peter Plaumann, Liudmila Sabinina, L. Sbitneva   +2 more
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Varieties Of Steiner Loops and Steiner Quasigroups

Canadian Journal of Mathematics, 1976
A Steiner Triple System (STS) is a pair (P, B) where P is a set of points and B is a set of 3-elenient subsets of P called blocks (or triples) such that for distinct p, q ∈ P there is a unique block b ∈ B with ﹛p, q) ⊂ b. There are two well-known methods for turning Steiner Triple Systems into algebras; both methods are due to R. H. Bruck [1].
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Quasi-Invariant and Invariant Functionals and Measures on Systems of Topological Loops and Quasigroups

Siberian Mathematical Journal, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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INFINITE IRREDUNDANT SYSTEMS OF IDENTITIES IN COMMUTATIVE MOUFANG LOOPS AND DISTRIBUTIVE STEINER QUASIGROUPS

Mathematics of the USSR-Izvestiya, 1988
Translation from Izv. Akad. Nauk SSSR, Ser. Mat. 51, No.1, 171-188 (Russian) (1987; Zbl 0615.20055).
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The geometric mean and B-loop quasigroups of the convex cone of positive definite matrices

Archiv der Mathematik, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment

Ca-A Cancer Journal for Clinicians, 2022
Jun J Mao,, Msce, Lorenzo Cohen, Karen M Mustian   +2 more
exaly  

A representation of parastrophs of loops and quasigroups

Discrete Mathematics and Applications, 2004
K.K. Shchukin, V.V. Gushan
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On check character systems over quasigroups and loops

2019
Summary: In this article we study check character systems that is error detecting codes, which arise by appending a check digit \(a_n\) to every word \(a_1a_2\cdots a_{n-1}\in Q^{n-1} \colon a_1a_2\cdots a_{n-1}\to a_1a_2\cdots a_{n-1}a_n\) with the check formula \((\dots((a_1\cdot\delta a_2)\cdot\delta^2 a_3)\dots) \cdot\delta^{n-2}a_{n-1})\cdot\delta^
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