Rom\u00e1n \u00c1lvarez (Universitat Aut\u00f2noma de Barcelona)<\/p>\n
Package Deal Theorems for Localizations over h-local Domains<\/em><\/p>\n Abstract: Let $R$ be a commutative ring with total ring of fractions $Q$, let $\\Lambda$ be a (not necessarily commutative) $R$-algebra, and let $M$ be a finitely generated right $\\Lambda$-module. For each maximal ideal $m$ of $R$, consider a (not necessarily finitely generated) $\\Lambda_m$-submodule $X(m)$ of $M_m$. For which such families is there a $\\Lambda$-submodule $N$ of $M$ such that $N_m=X(m)$? This question was answered by Levy-Odenthal for $R$ a commutative Noetherian ring of Krull dimension 1 under two consistency hypotheses:<\/p>\n 1. $X(m)=M_m$ for almost all maximal ideals $m$ of $R$;<\/p>\n 2. $X(m)\\otimes Q=M\\otimes Q$ for all maximal ideals $m$ of $R$.<\/p>\n They called these kinds of results Package Deal Theorems.<\/p>\n In this talk, I will give a version of this result for a larger class of domains, namely $h$-local domains, which were introduced by Matlis in the 1960s. $h$-local domains are commutative domains with the property that each non-zero element is contained in only finitely many maximal ideals of the ring and each non-zero prime ideal is contained in a unique maximal ideal of the ring. From results of previous work of Herbera-P\u0159\u00edhoda and the original techniques of Levy-Odenthal, I will conclude with a Package Deal Theorem for traces of projective modules over $h$-local domains.<\/p>\n","protected":false},"excerpt":{"rendered":" Rom\u00e1n \u00c1lvarez (Universitat Aut\u00f2noma de Barcelona) Package Deal Theorems for Localizations over h-local Domains Abstract: Let $R$ be a commutative ring with total ring of fractions $Q$, let $\\Lambda$ be a (not necessarily commutative) $R$-algebra, and let $M$ be a finitely generated right $\\Lambda$-module. For each maximal ideal $m$ of $R$, consider a (not necessarily … <\/p>\n