Results 41 to 50 of about 93 (80)
Determination of division algebras with 243 elements
, 2012 Finite nonassociative division algebras (i.e., finite semifields) with 243 elements are completely classified. Nine Knuth orbits were found, two of which are new.
Rúa, I.F. +2 more
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A parametrization of nonassociative cyclic algebras of prime degree
We determine and explicitly parametrize the isomorphism classes of nonassociative quaternion algebras over a field of characteristic different from two, as well as the isomorphism classes of nonassociative cyclic algebras of odd prime degree m when the ...
Pumplün, Susanne, Nevins, Monica
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On the right nucleus of Petit algebras [PDF]
, 2022 Let D be division algebra over its center C, let σ be an endormorphism of D, let δ be a left σ-derivation of D, and let R=D[t; σ, δ] be a skew polynomial ring.
Owen, Adam
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On the kernel and the nuclei of 8-dimensional locally compact quasifields [PDF]
, 2012 In this note we determine the nuclei of 8-dimensional real nonassociative division algebras and also study the corresponding substructures of 8-dimensional locally compact ...
Hähl, Hermann, Buchanan, Thomas
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Division algebras in linear Gr-categories
, 2014 : We study division algebras in an arbitrary linear Gr-category, i.e., a category of finite-dimensional vector spaces graded by a group with associativity constraint given by a 3-cocycle.
Van Oystaeyen, Freddy +2 more
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Nonassociative normed algebras: geometric aspects
, 1994 Introduction. The aim of this paper is to review some relevant results concerning the geometry of nonassociative normed algebras, without assuming in the first instance that such algebras satisfy any familiar identity, like associativity, commutativity ...
Rodríguez Palacios, Angel
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Real Flexible Division Algebras
, 1982 In this paper we classify finite-dimensional flexible division algebras over the real numbers. We show that every such algebra is either (i) commutative and of dimension one or two, (ii) a slight variant of a noncommutative Jordan algebra of degree two ...
Georgia M. Benkart +2 more
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How to obtain lattices from (f,σ,δ)-codes via a generalization of Construction A [PDF]
, 2017 We show how cyclic (f,σ,δ)-codes over finite rings canonically induce a Z-lattice in RN by using certain quotients of orders in nonassociative division algebras defined using the skew polynomial f.
Pumpluen, Susanne, S. Pumplün
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Some new classes of division algebras and potential applications to space-time block coding [PDF]
, 2014 In this thesis we study some new classes of nonassociative division algebras. First we introduce a generalisation of both associative cyclic algebras and of Waterhouse's nonassociative quaternions.
Steele, Andrew
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Nonassociative cyclic extensions of fields and central simple algebras [PDF]
We define nonassociative cyclic extensions of degree m of both fields andcentral simple algebras over fields. If a suitable field contains a primitive mth (resp., qth) root of unity, we show that suitable nonassociative generalized cyclic division ...
Brown, C., Pumpluen, S.
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