Classification of the finite dimensional absolute valued algebras having a non-zero central idempotent or a one-sided unity
نویسندگان
چکیده
منابع مشابه
On Finite-Dimensional Absolute Valued Algebras
This is a study of morphisms in the category of finite dimensional absolute valued algebras, whose codomains have dimension four. We begin by citing and transferring a classification of an equivalent category. Thereafter, we give a complete description of morphisms from one-dimensional algebras, partly via solutions of real polynomials, and a complete, explicit description of morphisms from two...
متن کاملMorphisms in the Category of Finite Dimensional Absolute Valued Algebras
This is a study of morphisms in the category of finite dimensional absolute valued algebras, whose codomains have dimension four. We begin by citing and transferring a classification of an equivalent category. Thereafter, we give a complete description of morphisms from one-dimensional algebras, partly via solutions of real polynomials, and a complete, explicit description of morphisms from two...
متن کاملA Note on Absolute Central Automorphisms of Finite $p$-Groups
Let $G$ be a finite group. The automorphism $sigma$ of a group $G$ is said to be an absolute central automorphism, if for all $xin G$, $x^{-1}x^{sigma}in L(G)$, where $L(G)$ be the absolute centre of $G$. In this paper, we study some properties of absolute central automorphisms of a given finite $p$-group.
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This paper deals with the determination of the absolute valued algebras with a nonzero idempotent commuting with the remaining idempotents and satisfying x2x = xx2 for every x. We prove that, in addition to the absolute valued algebras R, C, H, or O of the reals, complexes, division real quaternions or division real octonions, one such absolute valued algebra A can also be isometrically isomorp...
متن کاملAbsolute Valued Algebras.
An algebra A over the real field R is a vector space over R which is closed with respect to a product xy which is linear in both x and y, and which satisfies the condition X(xy) = ÇKx)y = x(ky) for any X in R and x, y in A. The product is not necessarily associative. An element e of the algebra A is called a unit element if ex=xe = x for any x in A. Given any subset B of A, dim B will denote th...
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ژورنال
عنوان ژورنال: Bulletin des Sciences Mathématiques
سال: 2010
ISSN: 0007-4497
DOI: 10.1016/j.bulsci.2009.03.001