‎Representation of a class of semisimple F-algebras as a topological product of primitive algebras

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Science, University of Payame Noor (PNU), Tehran, Iran.

2 Department of Basic Sciences, Faculty of Basic Science, Technical and Vocational University (TVU), Tehran, Iran

10.22091/maa.2026.16460.1062

Abstract

‎It is a classical theorem of Bonsall-Duncan that every semi-simple Banach algebra can be represented as a product of primitive Banach algebras‎. ‎In this paper‎, ‎we investigate the extent to which this result remains valid beyond the Banach algebra setting‎. ‎We first show that the usual product topology fails to preserve several desirable topological properties‎, ‎such as local boundedness‎, ‎metrizability‎, ‎and strong sequentiality‎. ‎Nevertheless‎, ‎we obtain a weaker version of the theorem for a class of semi-simple F-algebras‎, ‎namely the class of FFSS-algebras‎, ‎which properly contains the class of locally bounded complete algebras‎. ‎To obtain a stronger analogue of the classical theorem‎, ‎we focus on semi-simple locally bounded complete algebras‎. ‎By introducing a suitable product structure equipped with a different topology (the supremum norm topology)‎, ‎we establish a complete counterpart of the Bonsall-Duncan theorem for this class‎.

Keywords

Main Subjects

Measure Algebras and Applications

Articles in Press, Accepted Manuscript
Available Online from 11 July 2026

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