Approximation in the radical algebra ℓ1(ωn) when {ωn} is star-shaped

1983 ◽  
pp. 258-272 ◽  
Author(s):  
Marc P. Thomas
Keyword(s):  
Radical Algebra

scholarly journals A radical algebra without derivations

1959 ◽  
Vol 10 (4) ◽  
pp. 584-584 ◽  
Author(s):  
Donald J. Newman
Keyword(s):  
Radical Algebra

scholarly journals Projective schur algebras over a field of positive characteristic

1998 ◽  
Vol 58 (1) ◽  
pp. 103-106 ◽  
Author(s):  
Eunmi Choi ◽  
Heisook Lee
Keyword(s):  
Positive Characteristic ◽  
Similar Question ◽  
Schur Algebras ◽  
Schur Algebra ◽  
Radical Algebra ◽  
Field Of Positive Characteristic

If the characteristic of a field K is not zero then the Schur group S(K) = 0. In this paper we ask a similar question for the projective Schur group PS(K) and prove that the subgroup of PS(K) consisting of radical algebras is trivial. This disproves the conjecture that every projective Schur algebra is similar to a radical algebra.

Some results on finiteness of radical algebras

1970 ◽  
Vol 11 (3) ◽  
pp. 291-296
Author(s):  
Ahmad Mirbagheri
Keyword(s):  
Chain Condition ◽  
Finitely Generated ◽  
Radical Algebra ◽  
Finite Dimensional ◽  
Ascending Chain Condition ◽  
Algebra Over A Field

R denotes always a radical algebra over a field φ. A left ring ideal of R which is also a subvector space over φ is called a left algebra ideal of R. R is said to be left algebra noetherian if it satisfies the ascending chain condition for left algebra ideals. If dim R < ∞, then (i) R is finitely generated (ii) R is left alehra noetherian (iii) R is algebraic. Since the radical of an algebraic algebra is nil ([4] P. 19), conditions (i), (ii), (iii) are also sufficient for R to be finite-dimensional.

Subalgebras of modular annihilator algebras

1969 ◽  
Vol 66 (1) ◽  
pp. 5-12 ◽  
Author(s):  
B. A. Barnes
Keyword(s):  
Banach Algebra ◽  
Linear Functional ◽  
Linear Functionals ◽  
Radical Algebra ◽  
Complex Functions ◽  
Closed Subalgebra ◽  
Point Evaluations ◽  
Complex Sequences ◽  
Simple Algebras ◽  
Image Position

Throughout this paper we deal only with complex and semi-simple algebras. Let B be such an algebra. We denote the socle of B as SB. B is a modular annihilator algebra if B/SB is a radical algebra, i.e. if every element of B is quasi-regular modulo the socle of B; see (1) or (12). Now assume that B is a modular annihilator algebra and a Banach algebra. Then any semi-simple closed subalgebra of B is a modular annihilator algebra by ((4), Cor. to Theorem 4·2,). It is not true, however, that any semi-simple subalgebra A of B is a modular annihilator algebra, even when A is a Banach algebra in some norm. We give a simple example to illustrate this. Let A be the algebra of all complex functions f, continuous on the closed unit disk D in the complex plane, analytic in the interior of D, and such that f(0) = 0. A is a Banach algebra in the usual sup norm over D. Now consider the norm on A defined byLet B be the completion of A in this norm. A has an involution * defined by and also ‖ff*‖ = ‖f‖2 for all f ∈ A. Therefore B is a B*-algebra. It is not difficult to verify that the only non-zero multiplicative linear functionals on A which are continuous with respect to the norm ‖·‖, are the point evaluations at 1/n, n = 1, 2 …. It follows that every non-zero multiplicative linear functional on B is an extension of one of these point evaluations to B. Thus B can be identified with the algebra of all complex sequences which converge to zero.

Sign in / Sign up

Export Citation Format

Share Document