Document Type : Research Paper

Authors

• M. Hadinejad ¹
• M. M. Zahedi ¹
• A. Borumand Saeid ²

¹ Department of Mathematics, Graduate University of Technology University, Kerman, Iran

² Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

The present paper aims to study the notion of Stonean filters on equality algebras and discusses the connection between
these filters and other types of filters on equality algebras. We show that any implicative filter, positive implicative filter
and Boolean filter is a Stonean filter on equality algebras and by some counterexample, we show that the vice versa do
not generally hold. In addition, it is checked that the relations of Stonean filter with implicative filter, fantastic filter,
Boolean filter, prime filter, maximal filter, ultra filter and positive implicative filter on equality algebras, while the
implicative, positive implicative, Boolean and Stonean filters are equivalent together under the condition involutive on
an equality algebra. The concept of primary filter is introduced, and its relationship with the prime filter is investigated.
Finally, Stonean radical filter (Rads(F)) is introduced according to the concept of Stonean filter on equality algebras,
and we prove that under a suitable condition if F is a prime filter, then Rads(F) = F. Also, in this article, we provide
several examples to make the definitions clearer.

Keywords

• Equality algebra
• (Stonean
• implicative
• fantastic
• Boolean
• prime
• maximal
• primary
• Stonean radical) filter