%0 Journal Article
%T Strongly Zeo-product Preserving Maps on Normed Algebras Induced by a Bounded Linear Functional
%J Khayyam Journal of Mathematics
%I Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
%Z 2423-4788
%A Khoddami, Ali Reza
%D 2015
%\ 01/01/2015
%V 1
%N 1
%P 107-114
%! Strongly Zeo-product Preserving Maps on Normed Algebras Induced by a Bounded Linear Functional
%K (Jordan) zero-product preserving map
%K strongly (Jordan) zeroproduct preserving map
%K Arens product
%K polynomial equation
%R 10.22034/kjm.2015.12290
%X We introduce the notions of strongly zero-product (strongly Jordan zero-product) preserving maps on normed algebras. These notions are generalization of the concepts of zero-product and Jordan zero-product preserving maps. Also for a non-zero vector space V and for a non-zero linear functional f on V, we equip V with a multiplication, converting V into an associative algebra, denoted by Vf . We characterize the zero-product (Jordan zero-product) preserving maps on Vf . Also we characterize the strongly zero-product (strongly Jordan zero-product) preserving maps on Vf in the case where V is a normed vector space and f is a continuous linear functional on V. Finally, for polynomials in one variable x over Vf , we shall show that each polynomial of precise degree n ≥ 0, with non-zero constant term has precisely n-zeros (counted with multiplicity) in Vf . While, polynomials of precise degree n ≥ 2, with zero constant term have infinitely many zeros when dim(V) ≥2. This shows that the algebraic fundamental theorem for polynomial equations over an arbitrary algebra, is not valid in general.
%U http://www.kjm-math.org/article_12290_710c39152e24a4b3dbb3fcee40265094.pdf