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Generalized trace submodules and centers of endomorphism rings | | Justin Lyle
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1 Nov 2023 | | Abstract: | Let $R$ be a commutative Noetherian local ring and $M$ a finitely generated $R$-module. We introduce a general form of the classically studied trace map that unifies several notions from the literature. We develop a theory around these objects and use it to provide a broad extension of a result of Lindo calculating the center of $operatorname{End}_R(M)$. As a consequence, we show under mild hypotheses that in dimension $1$, the canonical module of $Z(operatorname{End}_R(M))$ may be calculated as the trace submodule of $M$ with respect to the canonical module of $R$. | | Source: | arXiv, 2311.00220 | | Services: | Forum | Review | PDF | Favorites | |
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