Semistar invertibility on integral domains

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After the introduction in 1994, by Okabe and Matsuda, of the notion of semistar operation, many authors have investigated different aspects of this general and powerful concept. A natural development of the recent work in this area leads to investigate the concept of invertibility in the semistar setting. In this paper, we will show the existence of a ``theoretical obstruction'' for extending many results, proved for star-invertibility, to the semistar case. For this reason, we will introduce two distinct notions of invertibility in the semistar setting (called $\star$--invertibility and quasi--$\star$--invertibility), we will discuss the motivations of these ``two levels'' of invertibility and we will extend, accordingly, many classical results proved for the $d$--, $v$--, $t$-- and $w$-- invertibility.

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Commutative Algebra, Algebraic Geometry, 13A15; 13E99; 13C13

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http://salesiana.dossiersoluciones.com/handle/123456789/72637

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0409514
 http://arxiv.org/abs/math/0409514

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arXiv