k[x]-modules and Core-Nilpotent endomorphisms
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914516815577088 |
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| author | Alonso, Diego Alba González, Javier Sánchez |
| author_facet | Alonso, Diego Alba González, Javier Sánchez |
| contents | Core-nilpotent endomorphisms over an arbitrary vector space form the largest subset of the ring of endomorphisms over that arbitrary vector space which admit a decomposition as sum of two endomorphisms satisfying the analogous properties as the well known core-nilpotent decomposition of matrices. In this paper we present a new description of core-nilpotent endomorphisms using the $k[x]-$module structure they define in the base vector space. Moreover, our approach provides us with a ``new'' generalized inverse that restricts to the well known Drazin inverse under certain conditions. Similarly, we present a generalized core-nilpotent decomposition for endomorphisms over arbitrary vector spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26712 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | k[x]-modules and Core-Nilpotent endomorphisms Alonso, Diego Alba González, Javier Sánchez Commutative Algebra 13C99, 13E99, 15A03, 15A04, 15A09 Core-nilpotent endomorphisms over an arbitrary vector space form the largest subset of the ring of endomorphisms over that arbitrary vector space which admit a decomposition as sum of two endomorphisms satisfying the analogous properties as the well known core-nilpotent decomposition of matrices. In this paper we present a new description of core-nilpotent endomorphisms using the $k[x]-$module structure they define in the base vector space. Moreover, our approach provides us with a ``new'' generalized inverse that restricts to the well known Drazin inverse under certain conditions. Similarly, we present a generalized core-nilpotent decomposition for endomorphisms over arbitrary vector spaces. |
| title | k[x]-modules and Core-Nilpotent endomorphisms |
| topic | Commutative Algebra 13C99, 13E99, 15A03, 15A04, 15A09 |
| url | https://arxiv.org/abs/2604.26712 |