Split exact sequences of finite MTL-chains

• J.L. Castiglioni ^[1] ; W.J. Zuluaga Botero ^[2]
  1. [1] Universidad Nacional de La Plata

     Universidad Nacional de La Plata

     Argentina

     
  2. [2] Universidad Nacional del Centro de la Provincia de Buenos Aires, Argentina
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 62, Nº. 2, 2021, págs. 295-304
• Idioma: inglés
• DOI: 10.33044/revuma.1787
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• Resumen

  • 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.