Abstract
In this paper, we show that the going up and lying over theorems hold in PMV-algebras, and we prove that every \(\cdot \)-prime ideal in a PMV-subalgebra is the intersection of a \(\cdot \)-prime ideal in the overalgebra with the subalgebra. Also, we show that if P is a \(\cdot \)-prime ideal of a unital PMV-algebra A and \(A^{\prime }\) is a subalgebra of A, having P as a maximal \(\cdot \)-ideal, then \(A^{\prime }/0_{P}(A)\) is a local PMV-algebra which is called the localization of A at P relative to \(A^{\prime }\) where \(0_{P}(A)\) is the intersection of all \(\cdot \)-prime ideals of A contained in P.
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We would like to thank the anonymous referees for their helpful comments and suggestions for the improvement of this paper.
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Banivaheb, H., Saeid, A.B. Localization of PMV-algebras. Soft Comput 22, 31–40 (2018). https://doi.org/10.1007/s00500-017-2690-8
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DOI: https://doi.org/10.1007/s00500-017-2690-8