An investigation on regular relations of universal hyperalgebras

Document Type : Research Paper


1 Department of Mathematics, Persian Gulf University, Bushehr, 75169, Iran

2 Department of Mathematics Yazd University Yazd, Iran


In this paper, by considering the notion of $\Sigma$-hyperalgebras for an arbitrary signature $\Sigma$, we study the notions of regular and strongly regular relations on a $\Sigma$-hyperalgebra, $\mathfrak{A}$. We show that each regular relation which contains a strongly regular relation is a strongly regular relation. Then we concentrate on the connection between the fundamental relation of $\mathfrak{A}$ and the set of complete parts of $\mathfrak{A}$.


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