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Semistar invertibility on integral domains

Marco Fontana·Giampaolo Picozza
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Abstract

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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Marco Fontana, Giampaolo Picozza. 2004-09-27. Semistar invertibility on integral domains. https://arxiv.org/abs/math/0409514

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