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arXiv · 1609.03272

On epicomplete $MV$-algebras

Anatolij Dvurečenskij·Omid Zahiri
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Abstract

The aim of the paper is to study epicomplete objects in the category of $MV$-algebras. A relation between injective $MV$-algebras and epicomplete $MV$-algebras is found, an equivalence condition for an $MV$-algebra to be epicomplete is obtained, and it is shown that the class of divisible $MV$-algebras and the class of epicomplete $MV$-algebras are the same. Finally, the concept of an epicompletion for $MV$-algebras is introduced, and the conditions under which an $MV$-algebra has an epicompletion are obtained. As a result we show that each $MV$-algebra has an epicompletion.

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Anatolij Dvurečenskij, Omid Zahiri. 2016-09-12. On epicomplete $MV$-algebras. https://arxiv.org/abs/1609.03272

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