Gorenstein properties of split-by-nilpotent extension algebras

• Pamela Suarez ^[1]
  1. [1] Universidad Nacional de Mar del Plata

     Universidad Nacional de Mar del Plata

     Argentina

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 67, Nº. 1, 2024, págs. 137-144
• Idioma: inglés
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• Resumen

  • Let A be a finite-dimensional k-algebra over an algebraically closed field k. In this note, we study the Gorenstein homological properties of a split-by-nilpotent extension algebra. Let R be a split-by-nilpotent extension of A. We provide sufficient conditions to ensure when a Gorenstein-projective module over A induces a similar structure over R. We also study when a Gorenstein-projective R-module induces a Gorenstein-projective A-module. Moreover, we study the relationship between the Gorensteinness of A and R.