منابع مشابه
On Multiplication Algebras
The basic properties of multiplication algebras of nonassociative algebras over rings are introduced, including a discussion of multiplication algebras of tensor products of algebras. A characterization of semisimple artinian multiplication algebras is given along with a discussion of the nature of the simple factors of a multiplication algebra modulo its Jacobson radical. A criterion distingui...
متن کاملMultiplication operators on Banach modules over spectrally separable algebras
Let $mathcal{A}$ be a commutative Banach algebra and $mathscr{X}$ be a left Banach $mathcal{A}$-module. We study the set ${rm Dec}_{mathcal{A}}(mathscr{X})$ of all elements in $mathcal{A}$ which induce a decomposable multiplication operator on $mathscr{X}$. In the case $mathscr{X}=mathcal{A}$, ${rm Dec}_{mathcal{A}}(mathcal{A})$ is the well-known Apostol algebra of $mathcal{A}$. We s...
متن کاملmultiplication operators on banach modules over spectrally separable algebras
let $pa$ be a commutative banach algebra and $ex$ be a left banach $pa$-module. we study the set $dec_{pa}(ex)$ of all elements in $pa$ which induce a decomposable multiplication operator on $ex$. in the case $ex=pa$, $dec_{pa}(pa)$ is the well-known apostol algebra of $pa$. we show that $dec_{pa}(ex)$ is intimately related with the largest spectrally separable subalgebra of $pa$ and...
متن کاملOn the Cluster Multiplication Theorem for Acyclic Cluster Algebras
In [3] and [13], the authors proved the cluster multiplication theorems for finite type and affine type. We generalize their results and prove the cluster multiplication theorem for arbitrary type by using the properties of 2–Calabi–Yau (Auslander–Reiten formula) and high order associativity. Introduction Cluster algebras were introduced by Fomin and Zelevinsky in [9]. By definition, the cluste...
متن کاملOn bilinear algorithms for multiplication in quaternion algebras
We show that the bilinear complexity of multiplication in a non-split quaternion algebra over a field of characteristic distinct from 2 is 8. This question is motivated by the problem of characterising algebras of almost minimal rank studied in [1] This paper is a translation of a report submitted by the author to the XI international seminar ”Discrete mathematics and its applications”. Definit...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1986
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1986-0816327-2