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Showing 1 to 11 of 11 for “"Moufang"”.
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Topics in Moufang Loops
<p>We will begin by discussing power graphs of Moufang loops. We are able to show that as in groups the directed power graph of a Moufang loop is uniquely determined by the undirected power graph. In the process of proving this result we define the generalized octonion loops, a variety of Moufang …
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Varieties of Nonassociative Rings of Bol-Moufang Type
<p>In this paper we investigate Bol-Moufang identities in a more general and very natural setting, \textit{nonassociative rings}.</p> <p>We first introduce and define common algebras. We then explore the varieties of nonassociative rings of Bol-Moufang type. We explore two separate cases, the first …
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The Near Normality of the Commutant of a Moufang Loop
… conditions under which the commutant of a Moufang loop is normal and related topics. We begin by giving relevant background on Moufang loops and normality. We then prove a theorem showing how close the commutant is to being normal: cR(x, y)R(x, y)R(x, y) = c. We then prove a couple of …
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Abelian Tits sets of index type
… rang 2 werden, onder een extra voorwaarde die 'Moufang' genoemd wordt, geclassificeerd door Tits en Weiss. Het classificeren van de Moufang gebouwen van rang 1, de zogenoemde Moufang verzamelingen, is nog een belangrijk openstaand probleem. Voor eigenlijke abelse Moufang verzamelingen, waarvoor …
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Zorn vector matrices over commutative rings and the loops arising from their construction
… Paige used to construct simple nonassociative Moufang loops over finite fields can, in fact, be done over any commutative ring with the proper adjustments. The resulting loops are still Moufang, but no longer simple in general. Given a commutative ring and an ideal of that ring, the loop …
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On Loop Commutators, Quaternionic Automorphic Loops, and Related Topics
… of quasigroups which are isotopic to commutative Moufang loops and prove their full characterization. Moreover, we define a new variety of quasigroups motivated by the semimedial quasigroups and show that they have an affine representation over commutative Moufang loops similar to the semimedial …
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Envolventes universales de álgebras de Sabinin
… coasociativas verificando la identidad de Moufang-Hopf. -estudio de las identidades que definen la variedad de las álgebras tangentes a lazos monoasociativos, una variedad de álgebras de Sabinin que generaliza las álgebras de Lie, Malcev y Bol. -extensión a característica arbitraria del …
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Open Innovation in the light of Patent Law.
… 1986, p. 62; Keukenschrijver, 2016b Rdn. 6-10; Moufang, 2017a Rdn. 15) An innovation can be created by an OI project. If this innovation fulfils the requirements of an invention, patent law is relevant. In this case, it can be checked whether the innovation of the OI project can lead to a …
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Sedenion extension loops and frames of hypercomplex 2[superscript n]-ons
… do not directly yield loops in the way that Moufang loops are obtained from octonions, the left loop of non-zero sedenions does contain new two-sided subloops as sedenion extensions. These loops are constructed abstractly as extensions of subloops L of the octonions. The chapter examines the …