Author:
Fuller K. R.,Nicholson W. K.,Watters J. F.
Abstract
If VK is a finite dimensional vector space over a field K and L is a lattice of subspaces of V, then, following Halmos [11], alg L is defined to be (the K-algebra of) all K-endomorphisms of V which leave every subspace in L invariant. If R ⊆ end(VK) is any subalgebra we define lat R to be (the sublattice of) all subspaces of VK which are invariant under every transformation in R. Then R ⊆ alg [lat R] and R is called a reflexive algebra when this is equality. Every finite dimensional algebra is isomorphic to a reflexive one ([4]) and these reflexive algebras have been studied by Azoff [1], Barker and Conklin [3] and Habibi and Gustafson [9] among others.
Publisher
Canadian Mathematical Society
Cited by
16 articles.
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1. Left Ideal Preserving Maps on Triangular Algebras;Iranian Journal of Science and Technology, Transactions A: Science;2019-11-18
2. SKEW POLYNOMIALS AND ALGEBRAIC REFLEXIVITY;Glasgow Mathematical Journal;2003-02
3. On reflexivity of direct sums;Proceedings of the American Mathematical Society;2000-04-28
4. Reflexivity of modules over QF-3 algebras;Communications in Algebra;1998-01
5. Local multiplications on algebras;Journal of Pure and Applied Algebra;1997-03