Generalized Fischer Groups and Algebras
نویسنده
چکیده
Introduction. In this paper we shall be concerned with the structure of the rational representation of certain sets of matrices, to which we give the name generalized Fischer sets. If K is any field, any fixed automorphism of K, and A any matrix with elements in K, we use the notation A* for the 0-automorph of A ; that is, the matrix obtained from A by subjecting each of its elements to the automorphism . Again, we denote by -4* the transposed 0-automorph A'* of A.
منابع مشابه
Addendum to the Paper "generalized Fischer Groups and Algebras"
The author regrets the omission, in a paper which recently appeared, of an important reference to a paper by N. Jacobson. Indeed Lemma I l i a of the author's paper, and its immediate consequence, Theorem I, are rather special cases (albeit independently obtained) of Theorem I of the latter paper. Accordingly Professor Jacobson's name should have appeared in the introduction along with those of...
متن کاملMODULE GENERALIZED DERIVATIONS ON TRIANGULAUR BANACH ALGEBRAS
Let $A_1$, $A_2$ be unital Banach algebras and $X$ be an $A_1$-$A_2$- module. Applying the concept of module maps, (inner) modulegeneralized derivations and generalized first cohomology groups, wepresent several results concerning the relations between modulegeneralized derivations from $A_i$ into the dual space $A^*_i$ (for$i=1,2$) and such derivations from the triangular Banach algebraof t...
متن کاملGeneralized additive functional inequalities in Banach algebras
Using the Hyers-Ulam-Rassias stability method, weinvestigate isomorphisms in Banach algebras and derivations onBanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)| le |f(alpha x+ beta y+gamma z)| .end{eqnarray}Moreover, we prove the Hyers-Ulam-Rassias stability of homomorphismsin Banach algebras and of derivations on Banach ...
متن کاملFixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications
In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the assumption of normality we establish common fixed point theorems for the generalized quasi-contractions with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$ in the set...
متن کاملApproximate solutions of homomorphisms and derivations of the generalized Cauchy-Jensen functional equation in $C^*$-ternary algebras
In this paper, we prove Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$eta mu fleft(frac{x+y}{eta}+zright) = f(mu x) + f(mu y) +eta f(mu z)$$ for all $mu in mathbb{S}:= { lambda in mathbb{C} : |lambda | =1}$ and for any fixed positive integer $eta geq 2$ on $C^*$-ternary algebras by using fixed poind alternat...
متن کامل