Revista de la
Unión Matemática Argentina
Split exact sequences of finite MTL-chains
J. L. Castiglioni and W. J. Zuluaga Botero
Volume 62, no. 2 (2021), pp. 295–304

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This paper is devoted to presenting ordinal sums of MTL-chains as a particular case of split short exact sequences of finite chains in the category of semihoops. This module theoretical approach will allows us to prove, in a very elementary way, that every finite locally unital MTL-chain can be decomposed as an ordinal sum of archimedean MTL-chains. Furthermore, we propose the study of MTL-chain extensions and we show that ordinal sums of locally unital MTL-chains are a particular case of these.