Displaying similar documents to “Loops embedded in generalized Cayley algebras of dimension 2 r , r ≥ 2 .”

Moufang loops arising from Zorn vector matrix algebras

Andrew Wells (2010)

Commentationes Mathematicae Universitatis Carolinae

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In “A class of simple Moufang loops”, Proc. Amer. Math. Soc. (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.

Identities and the group of isostrophisms

Aleš Drápal, Viktor Alekseevich Shcherbakov (2012)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we reexamine the concept of isostrophy. We connect it to the notion of term equivalence, and describe the action of dihedral groups that are associated with loops by means of isostrophy. We also use it to prove and present in a new way some well known facts on m -inverse loops and middle Bol loops.

Schreier loops

Péter T. Nagy, Karl Strambach (2008)

Czechoslovak Mathematical Journal

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We study systematically the natural generalization of Schreier's extension theory to obtain proper loops and show that this construction gives a rich family of examples of loops in all traditional common, important loop classes.

Relatives of K-loops: Theory and examples

Hubert Kiechle (2000)

Commentationes Mathematicae Universitatis Carolinae

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A or is a Bol loop with the automorphic inverse property. An overview of the most important theorems on K-loops and some of their relatives, especially Kikkawa loops, is given. First, left power alternative loops are discussed, then Kikkawa loops are considered. In particular, their nuclei are determined. Then the attention is paid to general K-loops and some special classes of K-loops such as 2-divisible ones. To construct examples, the method of is introduced. This has been used...

Some remarks on simple Bol loops

Gábor P. Nagy (2008)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we make some remarks on simple Bol loops which were motivated by questions at the LOOPS'07 conference. We also list some open problems on simple loops.