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Abstract

In this paper, we introduce the notions of node, nodal filter and seminode in equality algebras and study some properties of them. First, we study the relation between nodes and other specific elements. Furthermore, by defining some operations on $N F (E)$ , which is the set of all nodal filters in an equality algebra E, we prove that $(N F (E), \land, \leftrightarrow, E)$ is an equality algebra. In fact, we show that $N F (E)$ is a Hertz algebra, BCK-algebra, Hilbert algebra, Kleene algebra and semi-De Morgan algebra. Then we investigate the relation among nodal filters and (positive) implicative, fantastic, prime, and boolean filters in any equality algebras. Finally, we study the relation between nodes and seminodes. And we prove the set of all seminodes SN (E) is a lattice, Heyting algebra and Hertz algebra under the conditions.

Keywords

Equality algebra node nodal filter seminode hertz algebra

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Nodal filters and seminodes in equality algebras

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