Journal of Mathematical Analysis and Applications, ( ISI ), Volume (479), No (1), Year (2019-6) , Pages (963-976)

Title : ( JB-algebras of rank zero )

Authors: somaye ghorbani poor , Shirin Hejazian ,

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A unital JB-algebra A is defined to be of rank zero if the set of invertible elements is dense in A. A non-unital JB-algebra A is said to be of rank zero if its unitization A ⊕R1 is so. We show that a unital JB-algebra A is of rank zero if and only if the set of elements with finite spectrum is dense in A if and only if every inner ideal of A admits an approximate identity (not necessarily increasing) consisting of projections. Moreover, we establish that zero rank is inherited by every closed ideal and every quotient algebra.


, JB-algebra, Rank zero, Real rank zero, Inner ideal
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author = {Ghorbani Poor, Somaye and Hejazian, Shirin},
title = {JB-algebras of rank zero},
journal = {Journal of Mathematical Analysis and Applications},
year = {2019},
volume = {479},
number = {1},
month = {June},
issn = {0022-247X},
pages = {963--976},
numpages = {13},
keywords = {JB-algebra; Rank zero; Real rank zero; Inner ideal},


%0 Journal Article
%T JB-algebras of rank zero
%A Ghorbani Poor, Somaye
%A Hejazian, Shirin
%J Journal of Mathematical Analysis and Applications
%@ 0022-247X
%D 2019