DERIVATIONS OF PRIME FILTER THEOREMS GENERATED BY VARIOUS $\cap $-STRUCTURES IN TRANSITIVE $GE$-ALGEBRAS | ||
| Journal of Algebraic Systems | ||
| دوره 12، شماره 1، آذر 2024، صفحه 59-78 اصل مقاله (173.33 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.11542.1583 | ||
| نویسنده | ||
| Sambasiva RAO Mukkamala* | ||
| Department of Mathematics, MVGR College of Engineering, Vizianagaram, Andhra Pradesh, India. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| GE-algebra؛ GE-filter؛ prime filter؛ maximal filter؛ commutative closed set | ||
| مراجع | ||
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