Battaglia, M. (1990). Annihilators in JBalgebras. Mathematical proceedings of the Cambridge Philosophical Society, 108(2), pp. 317323. Cambridge University Press 10.1017/S0305004100069188

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Orthogonality is defined for all elements in a JBalgebra and Topping's results on annihilators in JWalgebras are generalized to the context of JB and JBWalgebras. A pair (a, b) of elements in a JBalgebra A is said to be orthogonal provided that a2 ∘ b equals zero. It is shown that this relation is symmetric. The annihilator S⊥ of a subset S of A is defined to be the set of elements a in A such that, for all elements s in S, the pair (s, a) is orthogonal. It is shown that the annihilators are closed quadratic ideals and, if A is a JBWalgebra, a subset I of A is a w*closed quadratic ideal if and only if I coincides with its biannihilator I⊥⊥. Moreover, in a JBWalgebra A the formation of the annihilator of a w*closed quadratic ideal is an orthocomplementation on the complete lattice of w*closed quadratic ideals which makes it into a complete orthomodular lattice. Further results establish a connection between ideals, central idempotents and annihilators in JBWalgebras.
Item Type: 
Journal Article (Original Article) 

Division/Institute: 
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics 
ISSN: 
03050041 
Publisher: 
Cambridge University Press 
Language: 
English 
Submitter: 
Marceline Brodmann 
Date Deposited: 
21 Jul 2020 11:48 
Last Modified: 
25 Jul 2020 12:23 
Publisher DOI: 
10.1017/S0305004100069188 
BORIS DOI: 
10.7892/boris.115926 
URI: 
https://boris.unibe.ch/id/eprint/115926 