Moufang buildings and twin buildings.
Moufang loops arising from Zorn vector matrix algebras
In “A class of simple Moufang loops”, Proc. Amer. Math. Soc. 7 (1956), 471–482, Paige used the vector matrix construction over fields to produce simple Moufang loops. The purpose of this paper is to generalize the construction to the class of commutative rings, and examine the Moufang loops arising in this fashion. Specific attention is paid to the construction over the ring of integers modulo four.
Moufang loops of odd order .
Moufang loops of odd order with non-trivial nucleus
It has been proven by F. Leong and the first author (J. Algebra 190 (1997), 474–486) that all Moufang loops of order where and are odd primes, are associative if , and
Moufang loops of order 243
We present a computer-assisted determination of the 72 non-isomorphic, non-associative Moufang loops of order 243. Some of their properties and distinguishing features are discussed.
Moufang loops of order coprime to three that cyclically extend groups of dihedral type
This paper completely solves the isomorphism problem for Moufang loops where is a noncommutative group with cyclic subgroup of index two and , is cyclic, , and is finite of order coprime to three.
Moufang planes and the groups EK6 and SL2(K), K a Cayley division algebra.
Moufang polygons. I: Root data.
Moufang semidirect products of loops with groups and inverse property extensions
We investigate loops which can be written as the semidirect product of a loop and a group, and we provide a necessary and sufficient condition for such a loop to be Moufang. We also examine a class of loop extensions which arise as a result of a finite cyclic group acting as a group of semiautomorphisms on an inverse property loop. In particular, we consider closure properties of certain extensions similar to those as in [S. Gagola III, Cyclic extensions of Moufang loops induced by semiautomorphisms,...
Moufang trees and generalized quadrangles.
Moyennabilité intérieure et extensions HNN
On présente des conditions suffisantes pour qu’une extension HNN soit intérieurement moyennable, respectivement CCI, qui donnent des critères nécessaires et suffisants parmi les groupes de Baumslag-Solitar. On en déduit qu’un tel groupe, vu comme groupe d’automorphismes de son arbre de Bass-Serre, possède des éléments non triviaux qui fixent des sous-arbres non bornés.
M-Solid Subvarieties of some Varieties of Commutative Semigroups
∗ The research of the author was supported by the Alexander v. Humboldt-Stiftung.The basic concepts are M -hyperidentities, where M is a monoid of hypersubstitutions. The set of all M -solid varieties of semigroups forms a complete sublattice of the lattice of all varieties of semigroups. We fix some specific varieties V of commutative semigroups and study the set of all M -solid subvarieties of V , in particular, if V is nilpotent.
Multi-mobs.
Multiparameter quantum function algebra at roots of 1.
Multiple Dirichlet series over rational function fields
Multiple left distributive systems
We describe the free objects in the variety of algebras involving several mutually distributive binary operations. Also, we show how an associative operation can be constructed on such systems in good cases, thus obtaining a two way correspondence between LD-monoids (sets with a left self-distributive and a compatible associative operation) and multi-LD-systems (sets with a family of mutually distributive operations).
Multiple Tilings of n-Dimensional Space by Unit Cubes.
Multiples of left loops and vertex-transitive graphs
Via representation of vertex-transitive graphs on groupoids, we show that left loops with units are factors of groups, i.e., left loops are transversals of left cosets on which it is possible to define a binary operation which allows left cancellation.
Multiplication, distributivity and fuzzy-integral. I
The main purpose is the introduction of an integral which covers most of the recent integrals which use fuzzy measures instead of measures. Before we give our framework for a fuzzy integral we motivate and present in a first part structure- and representation theorems for generalized additions and generalized multiplications which are connected by a strong and a weak distributivity law, respectively.
Multiplication, distributivity and fuzzy-integral. II
Based on results of generalized additions and generalized multiplications, proven in Part I, we first show a structure theorem on two generalized additions which do not coincide. Then we prove structure and representation theorems for generalized multiplications which are connected by a strong and weak distributivity law, respectively. Finally – as a last preparation for the introduction of a framework for a fuzzy integral – we introduce generalized differences with respect to t-conorms (which are...