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# On the length equalities for one-dimensional rings

Patil, DP and Tamone, G (2006) On the length equalities for one-dimensional rings. In: Journal of Pure and Applied Algebra, 205 (2). pp. 266-278.

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## Abstract

In this article we characterize noetherian local one-dimensional analytically irreducible and residually rational domains (R, mR) which are non-Gorenstein, the non-negative integer $\ell^\ast(R) = \tau R.\ell(R/\varrho)-\ell(\ddot{R}/R)$ is equal to τR-1 and $\ell(R/(\varrho+xR))=2$, where τR is the Cohen–Macaulay type of R,$\varrho$ is the conductor of R in the integral closure $\ddot{R}$ of R in its quotient field Q(R) and xR is a minimal reduction of $_m$ by giving some conditions on the numerical semi-group v(R) of R.

Item Type: Journal Article Copyright of this article belongs to Elsevier. Division of Physical & Mathematical Sciences > Mathematics 12 Mar 2007 19 Sep 2010 04:36 http://eprints.iisc.ernet.in/id/eprint/10308

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