Combinatorial polarization, code loops, and codes of high level.
Vojtěchovský, Petr (2004)
International Journal of Mathematics and Mathematical Sciences
Eugene C. Johnsen, Thomas Storer (1974)
Mathematische Zeitschrift
Fedir M. Sokhatsky (2004)
Discussiones Mathematicae - General Algebra and Applications
The article considers a problem from Trokhimenko paper [13] concerning the study of abstract properties of commutations of operations and their connection with the Menger and Mann superpositions. Namely, abstract characterizations of some classes of operation algebras, whose signature consists of arbitrary families of commutations of operations, Menger and Mann superpositions and their various connections are found. Some unsolved problems are given at the end of the article.
Tomáš Kepka (1978)
Acta Universitatis Carolinae. Mathematica et Physica
Jonathan D.H. Smith (1982)
Inventiones mathematicae
Tomáš Kepka, Petr Němec (1981)
Czechoslovak Mathematical Journal
Tomáš Kepka (1980)
Commentationes Mathematicae Universitatis Carolinae
Petr Němec (1988)
Commentationes Mathematicae Universitatis Carolinae
Martin Beaudry, Louis Marchand (2011)
Commentationes Mathematicae Universitatis Carolinae
We describe, in a constructive way, a family of commutative loops of odd order, , which have no nontrivial subloops and whose multiplication group is isomorphic to the alternating group .
Jan M. Raasch (2010)
Commentationes Mathematicae Universitatis Carolinae
Various commutators and associators may be defined in one-sided loops. In this paper, we approximate and compare these objects in the left and right loop reducts of a Catalan loop. To within a certain order of approximation, they turn out to be quite symmetrical. Using the general analysis of commutators and associators, we investigate the structure of a specific Catalan loop which is non-commutative, but associative, that appears in the original number-theoretic application of Catalan loops.
Michael Voit (1996)
Monatshefte für Mathematik
Sándor Radelecki (1991)
Czechoslovak Mathematical Journal
Cristea, Irina (2002)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
Milton Braitt, David Hobby, Donald Silberger (2012)
Mathematica Bohemica
In a groupoid, consider arbitrarily parenthesized expressions on the variables where each appears once and all variables appear in order of their indices. We call these expressions -ary formal products, and denote the set containing all of them by . If are distinct, the statement that and are equal for all values of is a generalized associative law. Among other results, we show that many small groupoids are completely dissociative, meaning that no generalized associative law holds...
Arkowitz, Martin, Gutierrez, Mauricio (1997)
International Journal of Mathematics and Mathematical Sciences
E.H. Moore (1898)
Mathematische Annalen
D.A. Robinson (1976)
Aequationes mathematicae
Václav Havel (1985)
Commentationes Mathematicae Universitatis Carolinae
Ivan Chajda (1996)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
Ivan Chajda, Radomír Halaš, František Machala (1997)
Czechoslovak Mathematical Journal
A ternary ring is an algebraic structure of type satisfying the identities and where, moreover, for any , , there exists a unique with . A congruence on is called normal if is a ternary ring again. We describe basic properties of the lattice of all normal congruences on and establish connections between ideals (introduced earlier by the third author) and congruence kernels.