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Topological Properties of Prime Filters and Minimal Prime Filters on a Paradistributive Latticoid

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  • Suryavardhani Ajjarapu
  • Ravikumar Bandaru
  • Ramakoteswara Rao Kotha
  • Rahul Shukla
  • Anwar Saleh Alwardi

Abstract

In this paper, we study the concepts of prime filters and minimal prime filters on a paradistributive latticoid (PDL) and discuss various results. In addition, we prove that the annihilator filter S• is equal to the intersection of all prime filters not containing S. Furthermore, we explore minimal prime filters and study certain results associated with them. We provide some equivalent conditions for a PDL to be relatively complemented. Additionally, we derive some topological properties of the space of prime filters and minimal prime filters.

Suggested Citation

  • Suryavardhani Ajjarapu & Ravikumar Bandaru & Ramakoteswara Rao Kotha & Rahul Shukla & Anwar Saleh Alwardi, 2024. "Topological Properties of Prime Filters and Minimal Prime Filters on a Paradistributive Latticoid," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2024, pages 1-12, November.
    • Handle: RePEc:hin:jijmms:1862245
    DOI: 10.1155/ijmm/1862245
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