The Journal of the Indian Mathematical Society

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Accessible Prime Ideals in Commutative Banach Algebras


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1 Department of Mathematics, Box 5054, Tennessee Technological University, Cookeville, TN-38505, United States
     

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A non-maximal closed prime ideal P in a commutative unital Banach algebra B is said to be accessible if P equals to the intersection of all closed ideals of B properly containing it. In this paper it is shown that a non-maximal closed prime ideal P is accessible if there exists a sequence {In} of ideals properly containing P is such that ∩In=P. Some non-trivial examples of accessible prime ideals are given.
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  • Accessible Prime Ideals in Commutative Banach Algebras

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Authors

Ramesh V. Garimella
Department of Mathematics, Box 5054, Tennessee Technological University, Cookeville, TN-38505, United States

Abstract


A non-maximal closed prime ideal P in a commutative unital Banach algebra B is said to be accessible if P equals to the intersection of all closed ideals of B properly containing it. In this paper it is shown that a non-maximal closed prime ideal P is accessible if there exists a sequence {In} of ideals properly containing P is such that ∩In=P. Some non-trivial examples of accessible prime ideals are given.