DERIVATIONS OF PRIME FILTER THEOREMS GENERATED BY VARIOUS $\cap $-STRUCTURES IN TRANSITIVE $GE$-ALGEBRAS

Document Type : Original Manuscript

Author

Department of Mathematics, MVGR College of Engineering, Vizianagaram, Andhra Pradesh, India.

Abstract

Properties of prime filters and maximal filters of transitive GE-algebras are investigated. An element-wise characterization is derived for the smallest GE-filter containing a given set. It is proved that the set of all GE-filters of a transitive GE-algebra forms a complete distributive lattice. Four different versions of a prime filter theorem are generalized in transitive GE-algebras. A necessary and sufficient condition is derived for a proper filter of a commutative GE-algebra to become a prime filter.

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References

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Journal of Algebraic Systems
Volume 12, Issue 1
September 2024
Pages 59-78

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