Abstract
We prove that if \({\mathcal{V}}\) is a modular variety such that the subdirectly irreducible algebras form a first order class in which there are no trivial subalgebras, then the class of directly indecomposable algebras of \({\mathcal{V}}\) is also first order.
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Badano, M., Vaggione, D. \({\mathcal{V}_{SI}}\) first order implies \({\mathcal{V}_{DI}}\) first order. Acta Math. Hungar. 151, 47–49 (2017). https://doi.org/10.1007/s10474-016-0676-0
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DOI: https://doi.org/10.1007/s10474-016-0676-0