Self-injective Right Artinian Rings and Igusa Todorov Functions |
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| Authors: | François Huard Marcelo Lanzilotta |
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| Institution: | 1. Department of Mathematics, Bishop’s University, Sherbrooke, Québec, Canada, J1M1Z7
2. Instituto de Matemática y Estadística Rafael Laguardia, Facultad de Ingeniería, Universidad de la República, J. Herrera y Reissig 565, CP 11300, Montevideo, Uruguay
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| Abstract: | We show that a right artinian ring R is right self-injective if and only if ψ(M)?=?0 (or equivalently ?(M)?=?0) for all finitely generated right R-modules M, where ψ, $\phi :\!\!\!\! \mod R \to \mathbb N$ are functions defined by Igusa and Todorov. In particular, an artin algebra Λ is self-injective if and only if ?(M)?=?0 for all finitely generated right Λ-modules M. |
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