‎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

Abstract

‎It is a classical theorem of Bonsall-Duncan that every semisimple 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. ‎First, we show that the usual product topology fails to preserve several important topological properties‎, ‎such as local boundedness‎, ‎metrizability‎, ‎and strong sequentiality‎. ‎Nevertheless‎, ‎we establish a weaker version of the theorem for a class of semisimple 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 semisimple locally bounded complete algebras‎. ‎By introducing a suitable product structure endowed with a different topology (the supremum norm topology)‎, ‎we establish a complete counterpart of the Bonsall-Duncan theorem for this class‎.

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References

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Measure Algebras and Applications
Volume 3, Issue 2 - Serial Number 5
December 2025
Pages 93-117

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